THE UNIVERSITY 
OF ILLINOIS 
LIBRARY 


The 
Frank Hall collection 
of arithmetics, 
presented by Professor 
H. L.. Rietz of the 
University of Iowa. 


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MATHEMAT {GS LIBRARY 


Return this book on or before the 
Latest Date stamped below. 


University of Illinois Library 


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MUL 24 | 


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Che Mormal Course in umber 


First Steps in Arithmetic 


BY 


Pia Asi PlER ECE 


SUPERVISOR OF PRIMARY GRADES, PUBLIC SCHOOLS, 


PROVIDENCE, R. I. 


SILVER, BURDETT AND COMPANY 
New YorK ... BOSTON . - . CHICAGO 


1899 


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Copyright, 1899 — 


By SILVER, BURDETT AND COMPANY 


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MATHEMATICS LIBRARY 


SUGGESTIONS TO TEACHERS. 


lives book is intended for the use of children oi the second school year, and cov- 

ers the fundamental processes through numbers to twenty. Both in the selection 
and sequence of subject matter the order of the development of the number sense in 
children has been carefully considered. In the development of the lessons, care has 
been taken to insure a clear perception and a firm grasp of the number facts which 
are the tools of all arithmetical work, and to develop the power to see both with eyes 
and mind the relations of quantities to each other, which is the basis of the power to 
apply knowledge. 

The lessons are of three kinds, — those not intended for the children at all, but 
meant as suggestions of method for the teacher, in introducing a new subject; those 
which are to be used by the children after preparation by the teacher; and those 
which may be taken at once by the class. 

To the first class belong the lessons teaching tens and ones, the first lessons in 
measures of all kinds, and the lessons directing the children to work, — draw, cut 
lay tables, ete. 

To the second class belongs apart of the lessons illustrated by tablets, measures, 
fractional parts, ete. When such lessons introduce a new principle, they should be 
preceded by a concrete lesson of instruction without books. When, however, they 
teach only new fucés illustrating principles previously taught, they may be taken at 
once by the class. 

To the third class belong all lessons which are applications of facts and principles 
already taught. Here the children should be left free, as only by making their own 
applications do they gain the power and the habit of making use of knowledge. If 
pupils fail in the problem work, it is due either to incompleteness of knowledge of 
facts or principles, or lack of power to image conditions and see relations. In the 
first case they need more instruction and practice of the kind which precedes the 
problems, and in the second case they should themselves diagram the conditions to 
strengthen the power to picture them. 


MATERIAL. 


The knowledge of both number facts and relations of quantities should have a 
concrete basis, but the material should vary according to the nature of the truth to 
be developed. Mere number facts — addition, subtraction, multiplication, division, 
fractional parts, and relations of numbers — may all be easily taught with the sim- 
plest objects, but the greatest_use_of these number facts in life is to represent, 
relations of quantities. It is the lack of mental power to see-these relations of 
quantities, and fit to them the corresponding relations of numbers, that prevents 
children from knowing whether to add or subtract, multiply or divide. It is, there- 
fore, necessary that this power should be developed side by side with the power to 
manipulate figures. Dry and liquid measures, long and-square measures, rectangles, 
det-fiocks olfer the best possible material for this purpose. Each school should be 
provided with the measures, and their values and relative values should be taught 
with the objects themselves and not with pictures. The use of pictures is to repre- 
sent and recall, not to replace the objects. 


4654 


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+ SUGGESTIONS TO TEACHERS. 


REVIEWS. 


In the development of each new subject, great care has been taken to introduce 
in abundance the facts previously taught, and in such a manner as to provide for 
their retention without tedious repetition and without interfering with the promi- 
nence which should be given to the new. The addition examples given just before 
leaving 11, 12, etc., review all additions already taught if added from the bottom up- 
ward. If they are used by the teacher as dictations, they should be given in the same 
order. 


WRITTEN EXERCISES. 


Ample provision has been made for the written work of the children in the belief 
that it is far better for children’s eyes to work from book to paper or slate than from 
blackboard, and in the hope of saving the teachers much blackboard work. Most of 
the written work should be first read in the class to insure its accuracy. At this age 
children do not need to write to show the teacher what they know, — that all comes 
out in the class work, —- but to practise putting down what they know, neatly, accu- 
rately, and with increasing rapidity. Many of the written exercises should be finally 
used as dictations. 


WORK OF THE FIRST YEAR. 


It is supposed that pupils beginning this book have had some number work in 
the first year. This work should be of the broadest, simplest, and most informal 
kind, conforming to the child’s own ideas. The power to count goes far ahead of 
the ability to recognize the number of objects in a group, and that in turn precedes 
the power to recognize the groups in a number. Comparison for difference pre- 
cedes the idea of comparison for proportion. Formal statements of number facts 
are not natural to children at any time, and should not be imposed upon them until 
long familiarity with the fact gives life and meaning to the statement. 

The number lessons in the first school year should be conversational exercises in 
which the children count the objects present, — children, chairs, window-panes, pen- 
cils, etc.; count abstractly; recognize numbers in groups not exceeding ten; separate 
numbers not exceeding ten into two groups; measure lengths in yards, feet, and 
inches ; build lengths not exceeding a foot with inch, two-inch, three-inch, four-inch, 
five-inch, and six-inch sticks; compare groups and lengths for differences; build 
rectangles with square inches; learn the names of halves, thirds, and fourths; 
and compare lines, surfaces, and numbers for proportion as children are able to 
comprehend. 

No figure or written work is desirable during the first year. Drawing, cutting, 
and laying material can be used to advantage, 

Eee ks 


SECTION 


XII. 
XIII. 
XIV. 

XV. 


m1, 


XVII. 


CONTENTS. 


Addition and Subtraction of Numbers to Seven 


Addition and Subtraction of Numbers from Eight to Ten. 


Multiplication and Division of Numbers to Ten 
Fractional Parts of a Unit 

Fractional Parts of Numbers to Ten . 
Miscellaneous Review . 

Numbers from Ten to Twenty as Tens and Ones. 
Inches and Square Inches 

Eleven . 

Twelve . 

Thirteen 

Fourteen 

Fifteen . 

Sixteen. 

Seventeen, Eighteen, and Nineteen 

Twenty . 


Miscellaneous Review . 


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First Steps in Arithmetic 


a 


FIRST STEPS IN ARITHMETIC. 


Sa GE LONe I: 


ADDITION AND SUBTRACTION OF NUMBERS TO SEVEN. 


a b Cc d é e 
5 f 
: g h 7 | k 1 


1. a. Henry had five cents and earned two cents; how many 
cents had he then ? 


6. A man had four cows in one barn and one cow in another 
barn; how many cows had he in both barns ? 


c. If a lady has six buttons in one box and one button im 
another box, how many buttons has she in both boxes ? 


10 FIRST STEPS IN ARITHMETIC. 


d. If Susie sewed two buttons on her coat and two buttons 
on her dress, how many buttons did she sew on in all? 

e. George wrote four words on his slate and two words on 
paper; how many words did he write ? 

f. I bought a three-cent postage stamp and a two-cent postage 
stamp; how much did I pay for both ? 

g. What must I pay for two pencils at one cent each? 

h. What would two tops cost at three cents apiece ? 

i. If Lucy’s mother made five buttonholes in the morning 
and one in the afternoon, how many buttonholes did she make 
in all? 

7. Aman bought three horses last week and one this week ; 
how many horses has he now ? 

i. If George worked for a man four days last week and three 
days this week, how many days did he work in both weeks ? 

]. Fanny sewed two buttons on one shoe and one on the other 
shoe; how many buttons did she sew on? 


2. a. If John had seven marbles and gave away two, how 
many marbles had he left? 

>. If a man had five horses and sold one, how many had he 
left ? 

c. If I had seven sheep and one died, how many had I left? 
_ d. If Mary had four oranges and ate two, how many had 
she left? 

e. If there were six leaves on a twig and two fell off, how 
many leaves were left on the twig? 


ADDITION AND SUBTRACTION OF NUMBERS TO SEVEN. 11 


f. If there were five frogs on a stone and two jumped into 
the pond, how many were left on the stone ? 

g. George had two apples and ate one; how many had he 
left ? 

h. A farmer planted six trees and three of them died ; how 
many were left alive? 

i. There were six cakes on a plate and Willie took one from 
the plate ; how many were left ? 

j. Carrie had four roses and gave one to Jennie; how many 
roses had Carrie left ? 

k. There were seven apples on a branch and some one picked 
three of them; how many were left on the branch ? 


I. If George had three cents and lost one, how many cents 
had he left ? 


= a. If there were seven flowers in a vase and Bessie took 
out five, how many flowers were left in the vase ? 

>. If in a store were five chairs and four were sold, how many 
remained in the store ? 

c. If George had seven cents and spent six, how many cents 
had he left ? 

d. If a man had four dollars and spent two, how many dollars 
had he left ? 

e. Six little girls were standing and four of them sat down; 
how many were left standing? 


f. If a man had five horses and sold three, how many horses 
had he left ? 


12 FIRST STEPS IN ARITHMETIC. 


g. Two little girls were looking out of a window and one of 
them went away; how many were left at the window ? 

h. If Johnnie had six marbles and gave three to his little 
brother, how many had he left ? 

2. If 1 could see six ducks on a pond and five went out of my 
sight, how many could [I still see ? 

j. If there were four boats tied to a wharf and a man took off 
three, how many boats were left ? 

k. John brought im seven baskets of wood; since that, his 
mother has used four of them. How many baskets are left ? 


l. If three boys were playing together and two went home, 
how many were left ? 


4. a. Beginning at the left of the tablets, make a number 
story for each tablet, beginning with the upper number. 

6. Make a number story for each one, beginning with the lower 
number. 

c. Make a number story for each one, taking away the upper 
number. 

d. Make a number story for each one, taking away the lower 
number. 

e. Beginning with the left-hand tablet, add together the dots 
in each one, beginning at the top. 


(Recite: Five and two are 2) 

f. Repeat, beginning with the lower number. 

g. Take away the upper number. (Recite: Seven less five 
:) 


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Sr 


ADDITION AND SUBTRACTION OF NUMBERS TO SEVEN. 18 


h, Take away the lower number. 

7. Beginning at the left, give at sight the number of dots on 
each tablet. 

7. Read these words: One, Two, Three, Four, Five, Six, Seven, 
one, two, three, four, five, six, seven, and, less, 1s, are. 


- 


WRITTEN EXERCISES. 


a. Write the words: One, one, Two, two, Three, three, Four, 
four, Five, five, Six, six, Seven, seven, and, less, is, are. 

6. Beginning with the left-hand tablet, write the addition table, 
beginning with the upper number. x. Five and two are seven. 

c. Write the addition table, beginning with the lower number. 


d. Write the subtraction table, beginning at the left, taking 
away the upper number. Jz. Seven less five is two. 


e. Take away the lower number. 


Copy and complete : 


Four and one are Six less three is 


Seven less three is Five and one are 


One and three are 


Three and three are 


Seven less two is 


Five less four 1s 


One and six are 


Two less one is 


Four less two 1s 


Two and two are 


Four and three are Two and five are 


Five less one is 


Three and one are 


Seven less six is 


Six less four is 
Two and one are 


Three and two are 


FIRST STEPS IN ARITHMETIC. 


Seven less one is Four and two are 


Five less three is 


Five less two is 
Four less three 1s b One and five are 


Four less one is 


Seven less five is 


One and one are Six less two is 


Three and four are Three less-one is 


One and two are 


Six less five 1s 
Six less one is 


Two and four are 
Seven less four 1s 


Five and two are 


One and four are Two and three are 


Three less two is 


Six and one are 


Draw pictures showing : 
Four wheels and three wheels. 
Three tops and three tops. 
Two kites and three kites. 
Five stars and two stars. 
Two rings and one ring. 
One bottle and five bottles. 
Two boxes and two boxes. 
One cat and one cat. 
Two cups and four cups. 
Six balls and one ball. 
Four squares and one square. 
One doll and three dolls. 


NUMBERS FROM EIGHT TO TEN. LD 


SECTION II. 


ADDITION AND SUBTRACTION OF NUMBERS FROM EIGHT TO TEN. 


a b c d € Ie g 
h 2 5 k l m 


5. a. A lady has seven pies in the cupboard and one on the 
table ; how many pies has she ? 

b. If a milkman sold four quarts of milk to one man and 
six quarts to another, how many quarts did he sell to both ? 

c, If there are two ducks on the pond and seven ducks on the 
bank, how many ducks in both places ? 

d. If a man had eight horses and bought two more horses, 
how many horses had he then ? 

e. There are two trees in my garden and six trees in ny 
sister's garden ; how many trees in both our gardens ? 

f. Tf there are three apples im one dish and seven apples in 
another dish, how many apples are in both dishes ? 


16 FIRST STEPS IN ARITHMETIC, 


g. Johnnie has six cents in his pocket and three cents in his 
box ; how many cents has he? 

h. Julia has five roses and three pinks; how many flowers 
has she? 

7. There were nine people in a room and one man came in; 
show many people were there in the room ? 

j. In a class were four boys and five girls; how many pupils 
were in the class ? 

k. George had one cent and earned eight more; how much 
money had he then ? 

/. Charles has five cents and Henry has five cents ; how much 
money have they both ? 

m. A man bought four books in one store and four in another 
store; how many books did he buy in both stores ? 


6. a. John had eight marbles and lost one; how many had 
he left ? 

b. Lucy had ten cents and spent six; how many had she 
left ? 

c. Henry had nine peaches and gave away seven; how many 
had he left? 

d. A man planted ten trees and two of them died; how many 
of the trees lived ? 

e. Mr. Brown had eight sheep and sold six of them; how 
many sheep had he left ? 

Ff. Mrs. Smith went shopping with ten dollars and spent seven 
dollars ; how much money had she left ? 


NUMBERS FROM EIGHT TO TEN. 17 


g. There were nine peaches on a tree and I picked three of 
them; how many peaches were left on the tree ? 

h. Y had eight dollars and spent three dollars; how much 
money had [I left ? 

i. There were ten apples in a dish and Will took one out ; 
how many apples were left in the dish ? 

7. If I had nine dollars and spent five dollars for a table and 
the rest for a chair, what did the chair cost ? 

k. If there were nine spoons in the spoonholder and I took 
out eight, how many were left? 

i. There were ten pins in a cushion and I took out five ; how 
many were left im the cushion ? 

m.. Henry had eight cents and bought a top for four cents; 
how many cents had he left? 


7. a. A man had eight watches and sold seven; how many 
had he left ? 

b. There were ten oranges in a dish and four were eaten ; 
how many were left ? 

c. If George had nine apples and ate two, how many had he 
left ? 

d. If a man had ten horses and sold eight, how many had he 
left ? 

e. If George had eight marbles and lost two, how many had 
he left ? 

f. There were ten ships in the harbor and three sailed away ; 


how many were left ? 


18 FIRST STEPS IN ARITHMETIC, 


g. There were nine birds on a tree and six flew away ; how 
many were left? 

h. There were eight roses on a bush and Jennie picked five 
of them; how many were left ? 

i. There were ten cakes for supper and nine were eaten; how 
many were left? 

j. Lucy is nine years old and Carrie is four years younger; 
how old is Carrie ? 

k. George had nine flags and lost one; how many had he 
left ° 

/. There were ten boys playing ball and five went home ; how 
many were leit ? 

m. Henry found eight shells on the beach and gave his sister 
four; how many had he left ? 


8, a. Beginning at the left, make a number story for each 
tablet, beginning with the upper number. 

b. Make a number story for each one, beginning with the 
lower number. 

c. Make a number story for each one, taking away the upper 
number. 

d. Make a number story for each one, taking away the lower 
number. 

e. Add together the dots in the tablets, beginning at the 
top. 

f. Add together the dots in the tablets, beginning at the - 
bottom. | 


NUMBERS FROM EIGHT TO TEN. 19 


g. Give at sight the whole number of dots in each tablet. 
h. Take away the upper number. 
7. Take away the lower number. 
7. Read these words: Hight, Nine, Ten, ¢ight, nine, ten. 


WRITTEN EXERCISES, 


a. Write the words: Eight, eight, Nine, nine, Ten, ten. 

6. Beginning with the upper number in each tablet, write the 
addition table. 

c. Beginning with the lower number in each tablet, write the 
addition table. 

d. Write the subtraction table, taking away the upper number. 

e. Write the subtraction table, taking away the lower number. 


Copy and complete : 


Nine less four is 


Three and seven are 


One and eight are One and seven are 


Four and five are 


Nine less two is 


Hight less four is : Ten less four is 


Ten less nine is Eight and one are 


Four and six are Two and seven are 


Eight less one is Nine and one are 


Ten less two is 


Six and two are 


Nine less six is 


Five and five are 


Two and six are 


Hight less three is 


Five and four are Eight less five is 


20 


Ten less eight is 
Six and three are 
Seven and one are 
Hight less two is 
One and nine are 
Nine less eight is 
Four and four are 
Two and eight are 
Ten less six is 
Five and three are 
Ten less seven is 
Nine less three is 
Ten less five 1s 


9, Figures and Signs: 
0). 


Zero, 
One, 
Two, 
Three, 
Four, 


FIRST STEPS IN ARITHMETIC. 


en or 


Five, 
Six, 
Seven, 
Hight, 
Nine, 


OPIS EE BASE: cork 


Seven and three are 


Hight less seven is 


Nine less one is 
Six and four are 


Nine less five is 


Seven and two are 


Ten less one 1s 


Kight and two are 
Three and five are 


Hight less six is 
Ten less three 1s 
Nine less seven is 
Three and six are 


Ten, 
And, 
Less, 
Is, are 


NUMBERS FROM EIGHT TO TEN. 91 


DRILL TABLE. . 
5 3 3 
| 3 2 
b c d e S 
4 5 7 4 2 
| | 2 | 6 r; 
k l m n 0 
6 5 
3 3 
s t u v w Gs y 


a. Make a number story about each of the tablets above, add- 
ing the two numbers. | 

b. Make a number story about each of the tablets, taking 
away the upper number. 

c. Make a number story about each of the tablets, taking away 
the lower number. 

d. Recite the table of additions, beginning each tablet with the 
upper number. 

e. Recite the table of additions, beginning each tablet with, 
the lower number. 

f. Recite the table of subtractions, taking away the upper 
number. 


bo 
bo 


FIRST STEPS IN ARITHMETIC. 


g. Recite the table of subtractions, taking away the lower 
number. 


h. Give the sum of the numbers in each group at sight. 


TABLE FOR RECITATION, DICTATION, AND OCCUPATION. 


hee ig (Pee hag 6—4=? 1 Os ie ay §9—b5=7 
7—38=? i os 34+2=? 10—2=? 10—8=? 
34+3=? L--2 =? 7—1=? 9—li1=? 10—9=°? 
5—4=? oo = 7 5—2=? 8+5=? 5+4=—=? 
Jae ams (4 Ortal eerie Ai 5 =P 9—2=? 8—2=? 
24+-2=9 Sti=? 1—o =? o+5d=? eS kg 
4+3=? 4—2=?P 8+7=? A ere oe ei bee 
1+1i=? re Ba Nm 8—l=? 10—7=? 8—d=? 
Dee ier 4—1=? 6+8=? 44+5=? 7+2=? 
De ia eg 6—1=? 0 tea 9—6=? 846=7 
i—2=7 (pe ae 9—4=—? 6+4=—? 2 eS ye 
5—1=? yee ag 9 = lew 8—6=? 10—8=P 
5—3 =? iP bay 8—7T=? 8—4=? Adie 
3—1=? 2+5=? 8+2=—? 8—3=? LQ pier 
aT at er cere ab tuyere: | Rees yt apy iy 
14+4=? Oe vise G12 7 9—T7T=? (em 
6—53 7 ea 47? DES Sila 10 —4= FP 1) ee 
1-67 3 GF ery 5+3=—P FN Seat 9—8=? 


10. a. A man bought three cows of one man and two cows 
of another man; how many cows did he buy ? 


b. George had nine marbles and gave away three; how many 
had he left ? 


bo 


9 
Oo 


NUMBERS FROM EIGHT TO TEN. 


ce. In a field are five gray horses and three brown ones ; how 
many horses are in the field? 

d. George has seven cents in a box and three in his pocket ; 
how many cents has he? 

e. Henry had nine marbles and lost four ; how many had he 
left ? 

f. Lucy had ten cents and spent six; how many had she 
left ? 

g. There were nine birds on a tree and two flew away ; how 
many were left ? 

h. There were eight roses on a bush and Carrie picked four ; 
how many roses were left on the bush ? 

i. George had six cents and his father gave him two more; 
how many cents had he then ? 

y. Jessie has three dolls and Mary has three ; how many dolls 
have they both ? 

k. Lily wants a slate which costs seven cents; she has five 
cents; how many more cents does she need to pay for the slate ? 

1. John has seven marbles and Willie has four; how many 
more marbles has John than Willie ? 

m. Jennie bought a book for eight cents and paid for it with 
a ten-cent piece; how much change did she receive ? 

n. Carrie picked four roses and Jessie picked two ; how many 
roses did they both pick ? 

o. Joseph has ten marbles and Henry has five; how many 
more has Joseph than Henry ? 

p. Think of seven; separate it into two parts; how many in 
each part ? 


24 FIRST STEPS IN ARITHMETIC: 


g. Think of seven ; separate it into two parts; take away the 
smaller part ; what is left? 


r. ‘Think of seven; separate it into two parts; take away the 
larger part; what is left? 

s. Think of eight; separate it into two parts just alike ; what 
is In each part? 

t. Think of eight; separate it into two parts not alike; what. 
is in each part ? 

w. Think of eight; separate it into two parts; take away one 
part ; what is left ? 

v. Think of nine ; separate it into two parts; what is in each 
part ? 

w. Think of nine; separate it into two parts; take away one 
part ; what is left ? 

x. Think of ten; separate it into two parts just alike; what is 
in each part ? é 

y. Think of ten; separate it into two parts not alike; what 
is In each part? . 


z. Think of ten; separate it into two parts; take away one 
part ; what is left? 
WRITTEN EXERCISES. 


Write answers to the questions in this lesson. 
La, ad. 9 cows, 8+2= 65, 


MULTIPLICATION AND DIVISION OF NUMBERS TO TEN, 26 


SECTION III. 


MULTIPLICATION AND DIVISION OF NUMBERS TO TEN. 


Leas oe ie ge 


11. a. How many tablets are here ? 

6b. How many dots are on each tablet? 

c. Begin at the left and add the dots. 

d. How many dots in all? 

e. How many are five twos? 

f. How many dots are on four tablets? How many are four 
twos ? 

g. How many dots are on three tablets? How many are 
three twos? 

h. How many dots are on two tablets? How many are two 
twos ? 

7. Count by twos to ten. 

jy. Count backward by twos from ten to zero. 

k, Hight is how many twos? 

7. Four is how many twos? 

m. Ten is how many twos? 


n. Six is how many twos? 


26 FIRST STEPS IN ARITHMETIC. 


0. How many pencils at two cents each can I buy for four 
cents ? 


p. What is the cost of three oranges at two cents each ? 


q. Ii I can get two marbles for one cent, how many can I get 
for three cents ? 


r. If George, John, James, and Henry each have two apples, 
how many apples have they all? 


s. What must I pay for five pencils at two cents each ? 

7. What must you pay for four blank books at two cents 
each ? 

u. How many two-cent tops can I buy for six cents ? 

v. To how many boys can I give two cents each, if I give ten 
cents in all? 

w. What are three chairs worth at two dollars each ? 

z. A man had five children; he gave them each two apples; 
how many apples did he give them all ? 

y. At two dollars each how many chairs can be bought for 
eight dollars ? 

z. If two yards of cloth make an apron, how many aprons’ 
can I make from six yards ? 

Four times two means the same as four twos. How many are 
four times two? Two times two? Three times two? Five 


times two? How many twos are there in eight? in four? in 
teu tI six? 


MULTIPLICATION AND DIVISION OF NUMBERS TO TEN. 27 


WRITTEN EXERCISE. 


Three times two are Six 1s twos. 

Five times two are Kight is twos. 

Two times two are Two boys have eyes. 
Four times two are Four dogs have ears. 
Once two is Three girls have hands. 
Four is twos. Five men have feet. 
Ten is twos. 


PINTS AND QUARTS. 


Pint. Quart. 


12. a. How many pints does it take to fill a quart measure ? 
6. How many pint measures can I fill with a quart of milk ? 
c. How many pints are there in three quarts ? 

d. How many pints are there in five quarts ? 

e. How many pints are there in four quarts ? 

jf. How many pints are there in two quarts ? 

g. U have four quarts of milk; how many pints have I? 

h. I have two quarts of molasses; how many pints have I? 


7. Jennie has three quarts of vinegar; how many pints has 
she ? 


28 FIRST STEPS IN ARITHMETIC. 


7. Mr. Brown bought five quarts of cider; how many pints 
did he buy? | 

k. How many quart measures can I fill with four pints of 
milk ? 


7. How many quart measures can I fill with six pints ? 
m. How many can I fill with ten pints ? 
n. How many can I fill with eight pints ? 


WRITTEN EXERCISE. 


Ten pints equal quarts. Three quarts equal pints. 
Four quarts equal pints. Four pints equal quarts. 
Two pints equal quart. Two quarts equal pints. 
Five quarts equal pints. 1x pints equal quarts. 


Hight pints equal 


A ee eae 
oe 


13. a. How many are two and one? 


quarts. 


@ © @ 


6. Three is how many twos, and how many over? 
c. How many are two times two? 

d. How many are two times two, and one more? 
e. Five is how many twos, and how many over? 


é 


MULTIPLICATION AND DIVISION OF NUMBERS TO TEN. 29 


jf. How many are three times two ? 

g. How many are three times two, and one more ? 
h. Seven is how many twos, and how many over? 
7. How many are four times two? 

4. How many are four times two, and one more ? 
k. Nine is how many twos, and how many over? 


i. How many pencils at two cents each can I buy for three 
cents, and how many cents would I have left? 


m. How many days would seven apples last me if I ate two a 
day? 
n. How many quarts are there in five pints ? 


o. How many quarts are there in seven pints? in nine pints? 
in three pints ? 


p. How many trvo-dollar chairs can I buy for five dollars, and 
how many dollars left? for three dollars? for seven dollars ? for 
nine dollars ? 


g. How many hours would it take me to walk six miles if I 
walk two miles an hour? 


r. How long at that rate would it take me to walk three 
miles? four miles? five miles? eight miles? nine miles? ten 
miles ? 

s. How many two-dollar hats can be bought for nine dollars, 
and how many dollars left ? for three dollars? for seven dollars ? 
for five dollars ? 

t. How many tables at two dollars each can be bought for 
seven dollars? for five dollars? for three dollars? for nine 
dollars ? 


30 FIRST STEPS IN ARITHMETIC. 


u. How many two-cent tops can be bought for five cents? for 
three cents ? for seven cents ? for nine cents ? 


Four divided by two means How many twos are there m four ? 
Seven divided by two means How many twos are there in seven ? 


ORAL AND WRITTEN EXERCISE. 


Hight divided by two are 


Five divided by two are (two, and one over.) 


Three divided by two are 


Four divided by two are 


Two divided by two are 


Six divided by two are 


Nine divided by two are 


Seven divided by two are 


Ten divided by two are 


a. How many are three and one? 
; ae many threes are there in four, and how many over ? 
c. How many are three and two? 
d. How many threes are there in five, and how many over? 


MULTIPLICATION AND DIVISION OF NUMBERS TO TEN. 81 


e. How many are two threes ? 

J. Tlow many are two threes and one more ? 

g. Seven is how many threes, and how many over? 

h. How many are two threes and two more ? 

2. Kight is how many threes, and how many over? 

Jj. How many are three threes ? 

k. Wlow many are three threes and one more ? 

/. ‘Ten is how many threes, and how many over ? 

m. How many apples at three cents apiece can you buy for 
four cents ? 

n. How many three-cent pencils can you buy for five cents ? 
for six cents? 

0. How many pairs of boots at three dollars each can be 


bought for seven dollars ? 


p. How many oranges at three cents apiece can be bought for 
eight cents? for five cents? for nine cents? for ten cents ? 

gq. How many three-dollar hats can be bought for nine dollars ? 
for six dollars? for seven dollars? for ten dollars? for eight dol- 
lars? for five dollars ? 

r. If three yards of cloth will make a waist, how many waists 
can be made from nine yards? from six yards? from five yards? 
from eight yards? from ten yards? 

s. How many are two times three ? 


?. How many are three times three ? 


~ 


4. Six divided by three are how many ? 
v. Nine divided by three are how many ? 


w. Four divided by three are how many, and how many over ? 


32 FIRSE STEPS IN ARITHMETIC. 


x. Ten divided by three are how many, and how many over ? 
y. Kight divided by three are how many, and how many over ? 


z. Five divided by three are how many, and how many over ? 


ORAL AND WRITTEN EXERCISE. 


Two times three are 


Three times three are 


Five divided by three are 
Hight divided by three are 
Four divided by three are ; 


Six divided by three are 


Ten divided by three are 


Seven divided by three are 


Nine divided by three are ' 


Three divided by three are ' 


Two clover leaves have leaflets. 


sides. 


15. a. At four cents each, how many slates can you buy for 
five cents ? 


Three triangles have 


MULTIPLICATION AND DIVISION OF NUMBERS TO TEN. 33 


6. At four dollars each, how many chairs can you buy for six 
dollars ? 

c. At four cents each, how many bananas can you buy for 
seven cents ? 

d. How many fours are there in seven? six? five? 

e. How many are two times four ? 

jf. How many are two times four, and one? 

g. How many are two times four, and two? 

h. How many fours are there in eight? in nine? in ten? 


Gallon, 


7. How many quarts does it take to fill a gallon measure ? 

j. How many gallon measures will eight quarts fill ? 

k, Two gallons are how many quarts ? 

7. If a man has five quarts of milk and sells a gallon, how 
much milk has he left ? 

m. A gallon and two quarts are how many quarts ? 

n. Seven quarts is how much more than a gallon ? 

o. If John buys a gallon of milk and Henry buys three quarts, 
how many quarts have they both? 

p. Hight quarts are how many gallons ? 

g. Two gallons and one quart are how many quarts? 


7. Two gallons and two quarts are how many quarts ? 
3 


34 FIRST STEPS VINGA LLL aie. 


s. If George buys five quarts of milk and Charles five quarts, 
how many quarts have they both? How many gallons have 
they both ? 

t. Nine quarts are how many gallons ? 

a. ‘Two times four are how many ? 

v. How many fours are there in seven? in eight ? in ten? in 
six? in nine? in five? in four? 

w. If I can walk four miles in an hour, how long will it take 
me to walk eight miles ? 


w. If four yards of cloth will make a coat, how many coats 
can I make from ten yards, and what will I have left ? 


y. Ii I have nine tops, to how many boys can I give four 
each, and how many tops will I have left? 


z. What is the cost of two tops, if one top is worth four 
cents ? 


WRITTEN EXERCISE. 


Two times four are 


Seven divided by four are 


Six divided by four are 


Four divided by four are 


Eight divided by four are 


Ten divided by four are 


Nine divided by four are 
At four cents each, two bananas would cost cents. 


If four yards of cloth will make a coat, 
two coats. 


yards will make 


One gallon is 


quarts. 


© 
cn 


MULTIPLICATION AND DIVISION OF NUMBERS TO TEN. 


Two gallons are quarts. 


In five quarts are gallon and quart. 
In ten quarts are gallons and quarts. 
One gallon and three quarts are quarts. 
Two gallons and one quart are quarts. 


cr, 


Peck. 


16. a. How many pecks does it take to fill a bushel? to fill 
two bushels ? 

b. One bushel and one peck are how many pecks? 

c. One bushel and three pecks are how many pecks ? 

d. Five pecks are how many bushels ? 

e. Six pecks are how many bushels ? 

jf. Seven pecks are how many bushels ? 

g. If a man has two bushels of potatoes and sells two pecks, 
how many pecks has he left ? 

h. If a man has a bushel of apples and buys two pecks, how 
many pecks has he ? 

i. If there are two bushels of apples in one cellar and two 
pecks in another cellar, how many pecks are in both cellars? 

j. If a store has ten pecks of apples and sells two bushels, how 
many pecks of apples are left? 

k. Two bushels and one peck are how many pecks? 


36 FIRST STEPS IN ARITHMETIC. 


i. Nine pecks less one peck are how many pecks? How 
many bushels 1s that ? 

m. Henry had a bushel and two pecks of potatoes ; how many 
pecks had he im all? 

mn. A man had two bushels of apples and sold three pecks; 
how many pecks had he left ? 


o. There are three pecks of potatoes in one barrel and five | 
pecks in another barrel; how many bushels in both barrels ? 


p. Five pecks and four pecks are how many bushels ? 
q. Six pecks and three pecks are how many bushels ? 
r. ‘Ten pecks less two pecks are how many bushels ? 


bu. stands for bushel or bushels. pk. stands for peck or pecks. 


WRITTEN EXERCISE. 


Seven pk. are bu. and pk. 

Nine pk. are bu. and —— pk. 

Six pk. are bu. and pk. 

Ten pk. are bu. and —— pk. 

Hight pk. are bu. 

Two bu. and one pk. are pk. 

One bu. and three pk. are pk. 

Two bu. and two pk. are pk. 

One bu. and two pk. are pk. 

Four pk. and three pk. are bu. and pk. 
Five pk. and three pk are bu. 

Six pk. and three pk. are —— bu. and pk. 


MULTIPLICATION AND DIVISION OF NUMBERS TO TEN. 37 


17. a. Six is how many fives? Seven? Hight ? Nine? Ten? 

b. At five cents each, how many tops can you buy for six 
cents ? 

ce. At five dollars each; how many tables can be bought for 
seven dollars ? 


d. If I have eight buttons, to how many girls can I give five 
buttons, and how many buttons will I have left? 


e. If it takes five yards of cloth to make a skirt, how many 
skirts could I make from nine yards, and how many yards would 
I have left ? 

f. How many are two fives? 

g. If it takes five yards of cloth to make a skirt, how many 
skirts will ten yards make ? 

h. How many fives are there in ten ? 

i. Ten divided by five are how many ? 

j. Six divided by five are how many ? 

k. Seven divided by five are how many? 

i. Nine divided by five are how many? 

m. Hight divided by five are how many ? 

n. Five divided by five are how many ? 

o. How many fingers have we on each hand? 


p. How many fingers have we on both hands ? 


38 


FIRST STEPS IN ARITHMETIC. 


q. How many toes have we on each foot ? 

7. How many toes have we on both feet ? 

s. How many cents is a dime ? 

¢. How many five-cent pieces 1s a dime worth ? 
u. How many legs has a chair? 

v. How many legs have two chairs? 

w. How many sides has a triangle ? 

wz. How many sides have two triangles ? 

y. How many sides has a square? 


X 


. How many sides have two squares ? 


WRITTEN EXERCISE. 


Nine divided by five are 


Seven divided by five are 


Hight divided by five are 
Six divided by five are , 
Ten divided by five are 
Two times five are 


Two hands have fingers. 


Two feet have toes. 


A dime is worth 


five-cent pieces. 


7) 


MULTIPLICATION AND DIVISION OF NUMBERS TO TEN. 89 
@e9 
@e@e@e 
eee 


18. a. How many are six and one? six and two? six and 


three ? six and four? 
b. How many sixes are there in seven? in eight? In nine? in 
ten ? 
c. How many are seven and one? seven and two? seven and 
three ? 
d. How many sevens are there in eight? in nine? m ten? 
e. How many are eight and one? eight and two? 
f. How many eights are there in nine? in ten? 
g. How many are nine and one ? 
h. How many nines are there in ten ? 
Seven divided by six are how many ? 
j. Eight divided by six are how many ? 
k:. Nine divided by six are how many ? 
1. Ten divided by six are how many ? 


m. Kight divided by seven are how many ? 


=~, 
- 


n. Nine divided by seven are how many ? 


40 FIRST STEPS IN ARITHMETIC. 


o. ‘Ten divided by seven are how many ? 
p. Nine divided by eight are how many ? 
g. Ten divided by eight are how many ? 


7. Ten divided by nine are how many? 


x -- 


19. How many are two times two? Two times two are four 
is written 2 x 2 = 4. 


Read and write this table: 


2 5c | tee ee Die OR ean is Sea Oe arg OOSC 25 ee 
Se ae, ie eae ema 4 in Se hy 3 xX l=? 
BOK Ay tat Nera a 3 Aer Deen 


How many twos are there in four? Four divided by two are 
how many? Sour divided by two are two is written 4+ 2= 2. 


Read and write this table: 


i A A see Rite ee ep Ee an Dat tee OF 
Oeee  e ie es as A et ant C= 37 


How many twos are there in five ? 
Five divided by two are how many ? 


Five divided by two are two and one over 1s written 56 + 2 = 2, 
1 over. 


f 


MULTIPLICATION AND DIVISION OF NUMBERS TO TEN. 41 


Read and write this table: 


8+2=? Ty Sean ek 9+8=? OG ara... 
1-200 => £ 8+7=? 6+5=? Grid 4 P 
8+38=? b- o =r ara ee Qi § = 5 
fp smn a 9+4=? 7+4=°? 10+3=>? 
10 +—4=? 5. 2S 8 10°=6-=7 1)! 8s 2 
= ZS == 7? 19s = t | eh as | §+4= 7? 
Be mn) eae i, 8+5=? 9=+6=?7 Ee | iat 


9(). a. A man had 10 sheep; he sold 4 of them to one man 
and 3 of them to another; how many sheep had he left? 

). Henry had 8 apples; he gave 3 of them to George and 2 
of them to Carrie; how many apples had he left? 

c. Jessie bought a slate for 4 cents and a pencil for 1 cent ; 
she paid for them with a 10-cent piece; how much change did 
she receive ? 

d. Carrie went to the store with 10 cents; she bought 5 cents’ 
worth of paper and a lead pencil for 2 cents; how many cents 
had she left ? 

e. A lady had 10 oranges; she put 7 of them into a dish and 
ate 1; the rest she gave to her little girl; how many did the 
little girl have ? 

f. At 5 cents apiece, what would 2 tops cost ? 

g. Mary can knit 3 scallops in an hour; how many can she 
knit in 2 hours ? 

h. A man can walk 4 miles an hour; how far can he walk in 


2, hours ? 


42 FIRST STEPS IN ARITHMETIC. 


z. At 2 dollars each, what would 5 chairs cost ? 

j At 5 dollars each, what would 3 hats cost ? 

k. At 2 dollars each, how many chairs could I buy for 8 
dollars ? 

i. If you can walk 4 miles an hour, how many hours would it 
take you to walk 8 miles? 

it. How many separate triangles can you lay with 9 sticks ? 


i. How many squares could you lay with 8 sticks ? 


~_» 


o. How many bushels are there in 9 pecks? 

p. How many gallons are there in 10 qt.? 

q. How many quarts are there in 7 pt.? 

r. If 2 boys can do a piece of work in 8 hours, how long 
would it take 1 boy to do it? 

s. How many benches would it take to seat 10 people, if 5 
people can sit on each bench? 

t. At 3 cents apiece, how many oranges can you buy for 8 
cents ? 

u. At 4 dollars each, how many tables could you buy for 10 
dollars ? 

v. How many sides have 3 triangles ? 

w. How many feet have 2 horses ? 

z. How many ears have 5 boys? 

y. How many sides have 2 squares ? 

z. How many toes has 1 boy? 


FRACTIONAL PARTS OF A UNIT. 43 


SECTION IV. 


FRACTIONAL PARTS OF A UNIT. 


21. a. Into how many parts is the apple divided ? 


b. What is the name of each part ? 

c. Into how many parts is the circle divided ? 

d. Which part is the larger ? 

e. What is the name of each part? What part of a circle is 
a semi-circle ? 


jf. How is the square divided ? 


If anything is divided into two equal parts, each part is called 


one half. 


g.- How much of the triangle is dark? How much of it is 
hight ? 


44 FIRST STEPS IN ARITHMETIC, 


h. How much of the oblong is dark? How much of it is 
light ? 

i. If you could eat half of the apple, what would you have left? 

j. If the circle were a cookie and you ate half and Jennie ate 
half, how much would you both eat ? 

k. If it were a cheese and a man sold half of it, how much of 
it would he have left ? 

/. How many halves make a whole pie ? 

m. How many halves make one cheese ? 

n. How many halves make one orange ? 

o. If George ate half an orange this morning and half an 


orange this noon, how many oranges has he eaten ? 


p. If a man sold half a cheese yesterday and half a cheese 
to-day, how many cheeses has he sold ? 


g. If a lady bought half a bushel of potatoes last month and 
half a bushel this month, how many bushels of potatoes has she 
bought ? | 

ry. Aman sold half a peck of apples to one lady and half a peck 
to another lady; how many pecks of apples did he sell to both ? 

s. How many pints make a quart ? 

?. A pint is what part of a quart ? 

uw. One half apple and one half apple are how many apples? 

v. One orange less one half orange is what ? 

w. One half dollar and one half dollar are what ? 

a. One dollar less one half dollar is what ? 

y. One half and one half are how many ? 

z. One less one half is what ? 


FRACTIONAL PARTS OF A UNIT. 45 


WRITTEN EXERCISE. 


This is a semi-circle. A semi-circle is what part of 
a circle ? 

A pint is what part of a quart ? 

If mamma made a pie and we ate half of it for 
supper, there is of it left. 

If there is one half of a cake in the pantry and 
one half of a cake on the table, both halves are equal 


to 


Johnnie had one dollar and spent half a dollar. He had 


left. 


22. a. Into how many parts is this melon divided ? 
b. What is the name of each part ? 
c. Into how many parts is the circle divided ? 


d. Into how many parts is the oblong divided ? 


46 FIRST STEPS IN ARITHMETIC. 


If anything is diwided into four equal parts, each part is called 
one quarter, or one fourth. 


e. What part of the oblong is dark ? 

f. What part of it is light? 

g. What part of the circle is dark ? 

h. What part of it is light ? 

i. If I had an apple and ate one fourth of it, how much of it 
would I have left ? 

7. If a lady cut out one fourth of a pie, how much of the pie 
is left ? } 

k. Look at the two squares. What part of the first square is 
dark ? What part of the second ? 


l. What part of the first square is hght? What part of the 
second ? 


m. If I ate one fourth of my orange, what part of it is left ? 


n. If you ate three fourths of your apple and gave the rest to 
Jennie, what part of it did you give to Jennie ? 


o. If Carrie had one fourth of a dollar and Lucy had three 
fourths of a dollar, how many dollars had they together ? 


p. How many fourths are there in one apple ? 
g. One orange less one fourth of an orange is what ? 
7. One cheese less three fourths of a cheese is what ? 


s. Three fourths of a cake and one fourth of a cake are how 
many cakes ? 


?. How many quarts are there in a gallon ? 
u. A quart is what part of a gallon? 
v. Three quarts are what part of a gallon? 


FRACTIONAL PARTS OF A UNIT. 47 


w. If I had a gallon of milk and used one fourth of it, what 
part of it did I have left ? 

2. How many quarts did I use? How many quarts had I left? 

y. A peck is what part of a bushel ? 

z. Three pecks are what part of a bushel ? 


WRITTEN EXERCISE. 


There are 


quarts in a gallon, 
A quart 1s one 


of a gallon. 


There are pecks in a bushel. 


A peck is one of a bushel. 


Three fourths of a pie and one fourth of a pie are equal to 
If mamma baked a cake and we ate three fourths of it, we 
of it left. 

If Henry had a dollar and spent one fourth of it, he has 
of it left. 

If a grocer had a bushel of potatoes and sold a peck, he 
had of a bushel left. 

If a lady had a gallon of milk and used a quart, she had 


have 


of a gallon left. 


If George’s father gave him three quarters of a dollar and his 


mother gave him one quarter, he had 
If Carrie had an apple and gave one fourth of it to Jessie and 
ate three fourths of it, she had left. 


48 FIRST STEPS IN ARITHMETIC: 


ety 
A RNY f} Hetty 
Ly “AU AN 
Sy i 


aN 
EF) par ya a 4 if AY ° Mf 
ae Hi Mii gg \ / j/ Wy 
, SYN MY phi si Pg ew aN 
\S< ZA NMEA = 
AN Sat \} yy A WH Wee \ wy y ae 
. Z , L—_——— 
. WA ZS 


i 


23. a. Into how many parts is the square divided ? 
b. What do we call one part, when anything is divided into 


four equal parts ? 
e. What part of the square is dark? 
d. What part of it is light? 
e. Can you express it differently ? 
f. Look at the apple. Into how many pieces is it divided? 
g. Which would you rather have, the large piece or the two 
small ones ? 
h. What is the name of the large piece ? 
i. What is the name of each of the small ones? 
7. How many fourths are equal to one half? 
k. Tf a man sold one fourth of a cheese on Monday and one 
fourth on Tuesday, what part of the cheese has he sold? 
i, If we ate one fourth of a cake last night and one fourth to- 
night, what part of the cake is eaten ? 
m. If Susie spent one fourth of a dollar yesterday and one 


FRACTIONAL PARTS OF A UNIT. 49 


fourth of a dollar to-day, how much money did she spend in both 
days ? 

n. If a family burned one fourth of a ton of coal one week 
and one fourth of a ton the next week, how much coal did they 
burn in the two weeks? 

o. If a family bought one fourth of a bushel of potatoes one 
week and one fourth of a bushel the next week, how much did 
they buy in both weeks? 

p. If a man had one half a cheese and sold one fourth of the 
cheese, what part of the cheese had he left ? 

q. If a family had one half of a peck of apples and ate one 
fourth of a peck, what part of a peck had they left ? 

r. If Carrie had half a dollar and spent a quarter of a dollar, 
what had she left? 

s. John’s mother gave him half an apple and gave Henry a 
quarter of the apple; what part of the apple did she give them ? 

?. If a man sold half a cheese to one man and a quarter of a 
cheese to another man, what part of the cheese did he sell? 


u. If we used a quarter of a bushel of potatoes last week and 
half a bushel this week, how much did we use in both weeks ? 


v. If a man had three fourths of a cheese and sold half a 
cheese, what had he left ? 


w. If John had three quarters of a dollar and spent one quar- 
ter of a dollar, what had he left ? 
x. If a family had three fourths of a ton of coal, how much 


coal have they left when they have used one fourth of a ton? 


y. Ua lady had three fourths of a pie and her family ate one 
half a pie, what part of the pie was left ? 
4 


50 FIRST STEPS IN ARITHMETIC. 


z. If a boy had three fourths of a pound of candy and ate one 
fourth of a pound, how much has he left ? 


WRITTEN EXERCISE. 


One fourth of an apple and one fourth of an apple are 


One half of an orange and one fourth of an orange are 


Three fourths of a pound of tea less one fourth of a pound of 
tea 1s 


Three fourths of a pound of candy less one half a pound of 
candy 1s 


Carrie has one fourth of an orange; Lucy has one half of an 
orange; they both have 


24. a. Into how many equal parts is the circle divided ? 
the square ? the oblong? : 


When anything is divided into three equal parts, each part is called 
one third. 

b. What part of the circle is dark ? 

c. What part of the square is dark ? 

d. What part of the oblong is dark ? 

e. What part of the circle is light ? the square? the oblong ? 


FRACTIONAL PARTS OF A UNIT. 51 
J. Beginning with the circle, tell what part of each figure is 
light and what part is dark. 
g. Ii I spent one third of my money, what part of it had I 
left ? 


h. If a man lost one third of his money, what part of it had 
he left ? 


i. If George gave away one third of his marbles, what part of 
them had he left ? 


J. If a storekeeper had a bushel of potatoes and sold two thirds 
of them, what part of them had he left ? 

k. If one third of a cheese has been sold, what part of it is 
left ? 

i. If two thirds of a cheese have been sold, what part of it is 
left ? 


m. If a man sold one third of a cheese to one man and one 
third to another, what part of the cheese has he sold? What part 
of it has he left ? 


n, One third of a pie and one third of a pie are what part of a 
9 


pie ? 
0. One cake less one third of a cake is what part of a cake ? 
p. One cake less two thirds of a cake is what part of a cake? 


g. Two thirds of a pie and one third of a pie are what part 
of a pie? 


WRITTEN EXERCISE. 


One third of a cake and one third of a cake are 


Two thirds of a pie and one third of a pie are 


Two thirds of a cheese less one third of a cheese is 


o2 FIRST STEPS IN ARITHMETIC. 


One cheese less one third of a cheese is 


One apple less two thirds of an apple 1s 


John has one third of a pie and Henry has one third of a pie. 
They both have 


A man sold two thirds of a cheese to one man and one 
third to another man; he sold to both 
[ 
| | 


25. a. Into how many parts is the first square divided ? 


Se eS J 


6. What is each part called ? 

c. Into how many parts is the second square divided ? 
d. What is each part called? 

e. What are two parts called ? 

jf. What are three parts called ? 

g. Into how many parts is the third square divided ? 
h. What 1s each part called ? 

i. What are two parts called? 


7. If we rubbed out half of the first square, what part of it 
would be left ? 


ik. Tf we rubbed out three fourths of the second square, what 
part of it would be left ? 


7. If we rubbed out one third of the third square, what part of 
it would be left ? 


FRACTIONAL PARTS OF A UNIT. O38 


m. How much is one half and one fourth ? 

n. How much is one half and one half? 

o. How much is three fourths and one fourth ? 
p- How much is one fourth and one fourth ? 
g. How much is one third and one third ? 

ry. How much is one third and two thirds ? 

s. One less one half is how much ? 

¢. Three fourths less one fourth is how much ? 
w. One less one fourth ? 

v. One less three fourths ? 

w. One half less one fourth ? 

z. Three fourths less one half ? 

y. One less one third ? | 


z. One less two thirds ? 


ORAL EXERCISE. 


26. a. Carrie has one half dollar and Lucy has one half dol- 
lar; they both have 


b. George has one half of an apple and Henry has one fourth 
of an apple; they both have 


c. There are three fourths of a bushel of potatoes in one bar- 
rel and one fourth of a bushel in another; in both barrels there 


Is 


d. Jennie walked one fourth of a mile to school and one fourth 


of a mile home again; in all she walked 
e. George ate one third of a pie and Henry ate one third of a 
pie; they both ate : 


o+4 FIRST STEPS IN ARITHMETIC. 


f. Jessie studied two thirds of an hour on her arithmetic les- 
son and one third of an hour on her spelling lesson; she studied 


in all 
g. Alice had an apple and gave away one fourth of it; she 
had left ——. 


h. Mary had one dollar and spent three fourths of it; she had 
left 


7. Jessie had three fourths of a dollar and spent one fourth of 
a dollar; she had left 


7. There was a cake on the table; one half of 1t was eaten ; 
of it was left. 


k. A man had three fourths of a bushel of potatoes and sold 
half a bushel; he had left ; 


7. George had half a dollar and spent a quarter of a dollar; 
he had left 


mM. 2 storekeeper had a piece of cloth and sold one third of it ; 
he had left ; 


n. A family bought a barrel of flour; when they had used two 
thirds of it, of it was left. 


o. A man had two thirds of a nheesee he sold one third of a 
cheese and had left : 


WRITTEN EXERCISE. 


Copy some of the number stories in this lesson, filling the 
blanks. 


—— 


FRACTIONAL PARTS OF NUMBERS TO TEN. 5d 


27. One half is written 1 
One third is written 4 

One fourth is written 1. 
T'wo thirds is written 2. 
Two fourths is written 2. 
Three fourths is written 3. 


Illustrate these fractions by drawings or by circles cut into 
parts. 


+4 b+4 1-} 1-3 
+4 i+4 +-4 We 
b+4 1-4 $-4 i-3 
+4 1-4} P14 


Read the fractions above, giving answers. 
Write them without illustrations, giving answers. 


SECTION V. 


FRACTIONAL PARTS OF NUMBERS TO TEN. 


Peck. 


28. a. How many pints are in a quart ? 
6. A pint is what part of a quart ? 
c. One half of two pints is how many pints? 


56 FIRST STEPS IN ARITHMETIC. 


d. How many quarts make a gallon ? 

e. How many quarts are there in half a gallon? 
Jf. One half of four quarts is how many quarts ? 

g. How many quarts are in a peck ? 

h. How many quarts are there in half a peck ? 

i. One half of eight quarts is how many quarts? 

jy. One half of ten cents is how many cents ? 

k. If I divide six into two equal parts, how many are in each 

part ? 
7. What is one half of six? eight? two? four? ten? 


RU ene eee ica. 


m. Count by ones to three. 

n. Count by twos to six. 

o. Count by threes to nine. 

p. If I divide three cents into three equal parts, what is in 
each part ? 

g. What is one third of three ? 

r. If we divide six into three equal parts, what 1s in each 
part ? 

s. What is one third of six? 

¢. If we divide nine into three equal parts, what is in each 
part ? 

uw. What is one third of nine? 


Cnr 
=~] 


FRACTIONAL PARTS OF NUMBERS TO TEN. 


v. Count by ones to four. 

w. Count by twos to eight. 

x. If four is divided into four equal parts, what is in each 
part ? 

y. If eight is divided into four equal parts, what is m each 
part ? 

z. What is one fourth of four? of eight? 


WRITTEN EXERCISE. 


If anything is divided into two equal parts, each part is called 
one 


If anything is divided into three equal parts, each part is 
called one 


If anything is divided into four equal parts, each part is called 


one 


One half of two cents is 


One half of four apples is 


One half of six miles is 


One half of eight tops is 


One half of ten kites is 


One third of three dollars is 


One third of six chairs is 


One third of nine tables is 


One fourth of four bananas 1s 


58 FIRST STEPS IN ARITHMETIC. 


One fourth of eight oranges is 


One half of a quart 1s pint. 

One half of a bushel is pecks. 

One fourth of a peck is quarts. 

One half of a peck is quarts. 

One half of a gallon is quarts. 

One fourth of a gallon is quart. 

One fourth of a bushel 1s peck. 

Read and write this table : 

tof4=? of Sie = tone t AOL Diese HOLL eae 
Lo 2) Of10 == teu tot C= pe Oh ant eee 


29. a. Divide 3 apples equally among 3 children. What 
part of the apples does each child receive ? 

b. How many apples does each child receive ? 

c. How many apples do 2 children receive ? 

d. What is 3 of 3? 2 of 3? 

e. If 3 chairs are worth 3 dollars, what is 1 chair worth ? 

f. Divide 6 apples into 3 equal parts. How many apples 
are in each part ? 

g. How many apples are in 2 parts? 

h. What is 4 of 6? 2 of 6% 

?. If 3 dolls cost 6 dollars, what is the cost of 1 doll? of 2 
dolls ? 

j. Divide 9 apples into 3 equal parts. How many apples are 
in each part ? 


FRACTIONAL PARTS OF NUMBERS TO TEN. 09 


k. How many apples are in 2 parts ? 

l. What is 4 of 9? 2 of 9? 

m. If 3 tables cost 9 dollars, what is the cost of 1 table? of 2 
tables ? 

n. Divide 4 oranges equally among 4 children. How many 
oranges does each child receive ? 

0. How many oranges do 2 children receive? 3 children ? 

p- What is } of 4? 2 of 4? 8 of 4? 

g. In what other way can you express 2° 

r. It 4 pencils cost 4 cents, what is the cost of 1? of 2? of 3? 

s. Divide 8 oranges into 4 equal parts. How many oranges 
are In each part ? in 2 parts? in 3 parts ? 

t. What is } of 8? 2 of 8? 3 of 8? 

u. If 4 tables cost 8 dollars, what is the cost of 1 table? of 2 
tables? of 3 tables ? 

v. Divide 8 pencils into 8 equal parts. Each part is called 
one eughth. 

w. What is 1 of 8? # of 8? 2 of 8? 4 of 8? 8 of 8? £ of 8? 
< of 8? 

az. If 8 pencils cost 8 cents, what is the cost of 1 pencil? of 3? 
of 5? of 2? of 7? of 6? of 4? 


y. What part of the first square is dark ? 
the third? | 


z. } 18 equal to how many fourths? to how many eighths ? 


of the second ? of 


FIRST STEPS IN ARITHMETIC. 


SECTION VI. 


MISCELLANEOUS REVIEW. 


3Q. TABLES FOR RECITATION, OCCUPATION, AND DICTATION. 


a. 
tof4=? POL Vo ieee AcOWOle= a? ASOLO een, 
4010 c= or 27010 POs ae Le hee Zof 8=? 
Zo0of4=°? 2 OLA Lay COL ROR =r FOL Ges 
LUC) Reo heey + Ola ea SOlediaoee 20S 24 
SOLS =r $2 OL iceana? f OL Asay er Eicoy — M4 
tof 8=° tof 4=? AeOL 2) ah Sf Oletieaee 
b. 
2 yet oul ong Bo ee Dace ees OB -ho) seer 
[i ieee at 4—2=? 6—2=? 
3 oie 6—4=? let Qo ae o9—3=? 
8—1l=? ted =r Oil exe OOo ae 
1+ 8=? 6 ge es 14+3=? 2+6=? 
6 2 Sao oe ya eae mms Si "eae 
1 §+4=7? 8—2=? 8—6=? 
5+2=? 4t+6=? 9—3=? 4+5=? 
Oa nnt Reeenae 1 Oo eee aie BL ahs Ane ay 
ye ee 6+3=° 9—5=7? Dp Pee 
8—T=? 7—2=? 1+2=? G+ 4: 
Fj me GS eal he sie ANY saat lg SS ieee ut ecte. eceee 
De poe se LO Oe DNS a pes Meme ty 
Der td aan 2 Tsar 190\— 5-42 (fees a 
8—4=? es peed en Re, 01 ot 
AD loners ty = ee PA? ae Bremel © Se Ao pl pane 
Ge ane Tice lies 9 °—4 =" 9 9 — 1 = 


~~ ww “~ eo) 


MISCELLANEOUS REVIEW. 


10—7=: 
6—3s=1: 


ie ety 
108 = 
7 ae Tee 
Fh he 


10+6= 


7 ae [ean 


3—-2= 
10 +-4= 
> ee Ye 
Tp a 
9 = 3 
10+8= 
4+—+4= 
4+2=— 
7+-5= 
4+3= 
o9+4= 
a 


? 
p) 
? 


941 
147= 
8—1= 
4-3 


5 —1 = 


| 


10—2=: 


5+-5= 
6+3= 
Hh i bi 
10+10= 
8+-3= 
10+3= 
2 2-= 
By 28 Gem 
2a eA 
10 +5 = 
yA a 
6+6= 
De 
Ae er 


ol. Add at sight, giving results only: 


6 


5 


4 


6 
3 


[ro wa 


a 


| <> 


| On 


Or 


On 


a+ 
List 
10 — 


4 
i) 
a 
2 


| 


| 


61 


Fame ok 


[~I bo 


|o o 


1 
es 


FIRST STEPS IN ARITHMETIC. 


8 


Subtract at sight : 


10 

2 7 
9 9 
1 8 
ou 10 
1 i 
7 6 
a 5 
fi 

i Hy 
Multiply : 
i Pe a he 
Noms Gm He 
thee 
Divide: 
9—+-3=? 
py OS 


| o> o 


| or 


10 


| 0 


—— 


10 


lo 


| <o 


9 


lor 


ln 


|oo © 


2 
6 
3 1 
4 5 
6 4s 
> 1 
10 
2 
4, 
4. 3 
3) 
il 1 
7 6 
Z 1 
2 a ee 
Ds ny 
D ex Aeeoer 
6—-3s8=?7? 
§=—2=? 


7 1 
4) 8 
2 3 
a, 5 
4 10 
2 4 
4 9 
3 2 
9 8 
01 7 
9 8 
%, 2 
4 10 
1 9 
ep ese 
1x3=? 
3°X 372 
10 =) = 


NUMBERS FROM TEN TO TWENTY. 63 


SECTION VII. 


32. NUMBERS FROM TEN TO TWENTY 


“nv 3 oo - 


Ten ones are one ten. 


fil One ten and one one are eleven. 
|| One ten and two ones are twelve. 
ik II One ten and three ones are thirteen. 


fl | | One ten and four ones are fourteen. 


"iin | | | One ten and five ones are fifteen. 


All | | One ten and six ones are sixteen. 


4|\\\| | One ten and seven ones are seventeen, 
‘ | | || | One ten and eight ones are eighteen. 


64 FIRST STEPS IN ARITHMETIC. 


ti 


One ten and nine ones are mnetleen. 


ayo tens are twenty. 


_~ ww 
a sites ie 
ie 


Fal 


ee : 
—— EXERCISE (without books). 


_ net 


(Each child provided with two bundles of counters, ten in each bunch.) 


Lay one ten and five ones. How many did you lay? 

One ten and three ones. How many is it? 

One ten and two ones? How many? 

One ten and six ones. How many? 

One ten and eight ones. How many? 

One ten and four ones. How many? 

One ten and seven ones. How many? 

One ten and nine ones. How many? 

One ten and one one. How many? 

Two tens. How many? 

Lay fourteen. How many tens and how many ones did you 
lay ? 

Lay seventeen. How many tens and how many ones is seven- 
teen ? : 

Lay thirteen. How many tens and how many ones is thir- 
teen ? 

Lay sivteen. How many tens and how many ones is sixteen ? 


Lay eighteen. How many tens and how many ones 1s 
eighteen ? 


NUMBERS FROM TEN T0 TWENTY. 65 


Lay twelve. How many tens and how many ones is twelve ? 

Lay fifteen. How many tens and how many ones is fifteen ? 

Lay eleven. How many tens and how many ones is eleven ? 

Lay nineteen. How many tens and how many ones is nine- 
teen? 


Lay twenty. How many tens and how many ones is twenty ? 


do. Lay eleven. What did you er i 


Eleven is written 11 in figures. 


Lay twelve. What did you lay? 


Twelve is written 12 in figures. 


What do you suppose the 1 stands for? the 2? 
. Lay thirteen. What did you lay? 


Thirteen is written 13. 


What stands for the ones? What stands for the ten ? 


Lay all the numbers to twenty, one ata time, pupils telling what each 
number is in tens and ones, teacher writing the figures, and teaching that 
when a number has two figures the first figure at the right stands for ones, 
and the second for tens. 


The purpose of these lessons immediately following is quite different from the 
addition of groups below ten, and those to come later of groups giving a result 
greater than ten. Those illustrated by ¢ groups are simple combinations of digits, and 
must be memorized as facts upon which higher additions depend. Those illustrated 
in tens and ones depend on the facts below ten already learned and do not need to 
be drilled upon as facts, but can be seen asa principle and recited at sight if the 
principle is grasped and numbers below ten are thoroughly known. They can 
therefore be gone over rapidly, the one thing to be ke pt in mind being the corres- 
pondence between them and numbers below ten. 

5 


66 FIRST STEPS IN ARITHMETIC. 


ADDITION AND SUBTRACTION. 


34. Lay ten and one. q| 


Ten and one are how many? 
One and ten are how many? 
Eleven less one are how many ? 


Eleven less ten are how many ? 


Lay ten and two. ql 


Ten and two are how many ? 

Eleven and one are how many ? 

One and how many are twelve? 

Two and how many are twelve? Ten and how many? 
Eleven and how many ? 

Twelve less ten are how many? less two? less one? less 
eleven? less twelve? 


ORAL AND WRITTEN EXERCISE. 


ADDITION. 


10 1 11 10 
me 


] es 
|e 
| vo 


SUBTRACTION. 


1 11 11 11 2 12 12 12 12 12 
11 10 1 1 11 10 2 12 


| 
#e 


NUMBERS FROM TEN TO TWENTY. 67 


35. Lay ten and three. 4 II 


Ten and three are how many ? 

Eleven and two are how many ? 

Twelve and one are how many ? 

One and how many are thirteen? Three and how many? Ten 
and how many? Two and how many? Twelve and how many ? 
Eleven and how many ? 

Thirteen less ten are how many? less one? less three? less 
eleven? less two? less twelve? less thirteen ? 


ORAL AND WRITTEN EXERCISE. 


ADDITION. 
1 10 12 11 
2 1 3 gL 2 


SUBTRACTION. 


13 13 13 13 13 13 13 
1 2 3 10 1 11 2 12 13 


| os 


36. Lay ten and four. {i | | 


Ten and four are how many ? 
Eleven and three are how many ? 
Twelve and two are how many ? 
Thirteen and one are how many ? 


68 FIRST STEPS IN ARITHMETIC. 


One and how many are fourteen? Three and how many? Two 
and how many? Four and how many? Ten and how many? 
Twelve and how many? Eleven and how many? Thirteen and 
how many ? 


Fourteen less four are how many? less one? less twelve? 
less ten? less three? less thirteen? less two? less eleven ? less 
fourteen ? 


ORAL AND WRITTEN EXERCISE. 


ADDITION. 

1 3 2 10 11 13 1 
3 1 2 4 3 At 2 
SUBTRACTION. 

4 14 | 14 4 14 14 
1 1 ul 2 2 12 
4 14 aM! 4 14 14 
3 3 13 4 4 14 


37. Lay ten and five. 


Ten and five are how many? Eleven and four? Twelve and 
three? Thirteen and two? Fourteen and one? 


One and how many are fifteen? Eleven and how many ? 
Three and how many? Thirteen and how many? Four and how 
many? Fourteen and how many? Two and how many? Twelve 
and how many? Five and how many? Ten and how many ? 


NUMBERS FROM TEN TO TWENTY. 69 


Fifteen less one are how many? less eleven? less three? less 
thirteen ? less two? less twelve? less four? less fourteen? less 
five? less fifteen? less ten ? 


ORAL AND WRITTEN EXERCISE. 


ADDITION. 

10 1 11 9 12 3 13 4. 14. 
5 4 3 3 2 2 i al 
SUBTRACTION. 

5 15 15 5 15 15 5 15 
1 1 11 2 9 12 3 3 
15 5 15 5 5 15 15 
13 4 4 5 5 15 


ORAL EXERCISE. 


38. a. George had 10 pencils and found another; how many 
pencils had he then ? 


6. Henry had 15 cents and spent 2; how many had he left ? 
e. Cora had 11 books and Susie had 4; how many had they 
both ? 


d. Jennie earned 10 cents and Sarah earned 4 cents; how 
much did they both earn ? 


e. Laura had 14 cents and spent 3; how many cents had she 
left ? 


f. John walked 10 miles in the morning and 5 miles in the 
afternoon ; how far did he walk in all ? 


70 


FIRST STEPS IN ARITHMETIC. 


Make number stories about these : 


12 + 2 Uy wd g3) 15 — 3 15— 4 13 — 12 

1 Bes eas 11+1 14 — 3 14— 1 15 — 12 

12+ 1 11 +4 15—1 14 — 13 14 — 11 

138 + 2 13+ 1 13 —1 15 — 14 15 — 13 

114 2 12-1 15 — 2 14 — 12 13 — 11 

14+1 14—2 13 — 3 12 — 11 15 — 11 
EXERCISES. 


39. a. Add, giving results at sight: 

6. Add, putting 1 in place of *: 

*] mh onl all *3 “Al *4 WP a ia 
Be Oe A eB ae aU Oe 


2 8 ce ieee eee Nog eee moO 
EXERCISES. 
a. Subtract, giving remainders at sight : 
6. Subtract, puttimg 1 in place of * : 
PO Mar 
*3 *5 *] *3 #7 *4 *3 *5 *4 #3 
ay 5o oO 1 1 0 2 0 1 3 


Subtract : 
15 14. 
11 12 
13 15 
10 yee 


NUMBERS FROM TEN TO TWENTY. 


ORAL AND WRITTEN EXERCISE 


EXERCISE. 
14 12 
13 11 
11 14 
11 10 


Complete these additions: 


11 


14 


12 


14 


Complete these subtractions : 


15 


14 


14 


14 


12 


13 


10 


13 


10 


14 


12 


11 


11 


11 


15 


13 


13 


12 


13 


oe | 
cot 


{a 


72 FIRST STEPS IN ARITHMETIC. 


15—? =4 144—? =38 19° ee) 13—? =2 
14 a? ey 12 Log or es 1) — = 
12 TO ye) eee 13—? = tn 
To —a9 14 ee) 16 13°? sci 


ta tl | 15 eae 9 ae 1 a eek Ee Tipe ea 5 


40. Lay ten and six. q\| | ] 


Ten and six are how many ? 


Eleven and five? Twelve and four? Thirteen and three? 
Fourteen and two? Fifteen and one? 


One and how many are sixteen? Eleven and how many? 
Three and how many? Thirteen and how many? Two and how 
many? Twelve and how many? Five and how many? Fifteen 
and how many? Six and how many? Four and how many? Four- 
teen and how many? Ten and how many ? 


Sixteen less one are how many? less eleven? less three? less 
thirteen ? less five? less fifteen? less four? less fourteen? less 
six ? less sixteen? less ten ? less two? less twelve? 


ORAL AND WRITTEN EXERCISE. 


ADDITION, 

10 1 11 9 12 3 13 4 14 
6 2 5 4 4 3 3 2 2 
SUBTRACTION 
6 16 16 6 16 16 6 16 
1 1 11 2 9 12 3 3 


NUMBERS FROM TEN TO TWENTY. 73 


16 6 16 16 6 16 16 
13 4 t 14 i) i) 15 


41. Lay ten and seven. | 


Ten and seven are how many? Eleven and six? Twelve and 
five? Thirteen and four? Fourteen and three? Fifteen and two? 
Sixteen and one? 

One and how many are seventeen? Eleven and how many? 
Two and how many? Twelve and how many? Three and how 
many? Thirteen and how many? Seven and how many? Four 
and how many? Fourteen and how many? Five and how many? 


Fifteen and how many? Six and how many ? Sixteen and how 
many? Ten and how many ? 


Seventeen less one are how many? less eleven? less three ? 
less thirteen ? less five? less fifteen? less two? less twelve? less 
six? less sixteen? less ten? less seven? less seventeen? less 
four? less fourteen ? 


ORAL AND WRITTEN EXERCISE. 


ADDITION. 
Tis; 1 11 2 12 5) 13 
a 6 6 ) 5 * 


14 5 15 6 16 


| co 
| ex 
Pike es 
| bo 
= 
fy 


T4 FIRST STEPS IN. ARITHMETIC. 


SUBTRACTION. 


7 17 hd ff 17 LG 7 
Li Ae iy A eg 
17 17 7 17 17 7 CF 
Bi Vow 1ST Ah wale ag mele ets ade aS Ae 
17 aT ilve 17, 7 17 Li 
15 6 6 16 7 My 17 


4%, Lay ten and eight. i ] | | | | 


How many are ten and eight? eleven and seven? twelve and 
six ? thirteen and five? fourteen and four? fifteen and three? 
sixteen and two? seventeen and one ? | 

One and how many are eighteen? Eleven and how many? 
Five and how many? Fifteen and how many? Seven and how 
many ? Seventeen and how many? Two and how many? Twelve 
and how many? Six and how many? Sixteen and how many ? 
Four and how many? Fourteen and how many? Eight and how 
many? Three and how many? Thirteen and how many? Ten 
and how many ? 

Eighteen less one are how many? less eleven? less three? 
less thirteen? less seven? less seventeen? less four? less four- 
teen? less six? less sixteen? less eight? less eighteen? less two? 
less twelve? less five? less fifteen ? less ten ? 


NUMBERS FROM TEN TO TWENTY. 


-1 


Or 


ORAL AND WRITTEN EXERCISE, 


ADDITION. 

10 1 11 2 12 3 13 4 
RGR es ak ee Sy Be eB 4 
14 5) 15 6 16 fi 17 

4 3 3 2 2 1 1 

SUBTRACTION. 

8 18 18 8 18 18 8 18 

ee mo apa. 2 1G 18 58 
18 8 18 18 8 18 18 8 
eee ees 5 5 
18 18 8 18 18 8 18 18 
6 16 7 7 1% 8 8 18 


43. Lay ten and nine. ANN HTT 


Ten and nine are how many? Eleven and eight ? Twelve and 
seven? Thirteen and six? Fourteen and five? Fifteen and four? 
Sixteen and three? Seventeen and two? Eighteen and one ? 

One and how many are nineteen? Eleven and how many? 
Four and how many? Fourteen and how many? Six and how 
many? Sixteen and how many? Three and how many? Thirteen 


76 FIRST STEPS IN ARITHMETIC. 


and how many ? Seven and how many? Seventeen and how many ? 
Nine and how many? Two and how many? Twelve and how 
many? Eight and how many? Eighteen and how many? Ten 
and how many? Five and how many? Fifteen and how many ? 


Nineteen less one are how many? less eleven? less three? 
less thirteen? less five? less fifteen? less two? less twelve ? less 
eight? less eighteen? less nine? less nineteen? less six? less six- 
teen? less four? less fourteen? less seven? less seventeen? less. 
ten ? | 


ORAL AND WRITTEN EXERCISE. 


ADDITION. 
10 8 18 7 17 6 
9 wit “it 9 2 3 
16 5 15 4 14 3 
3 4 4 5 5 6 
13 2 12 1 11 
6 a a“ 8 8 
. SUBTRACTION, . 
9 19 19 9 19 19 
as 1 Lelie 2 ete oe 
9 19 19 9 19 Se 
ce 3 13 4 4 14 


NUMBERS FROM TEN TO TWENTY. feet 


9 19 19 9 19 19 
5 2 15 Sara 16 
Ny] 19 19 i) 19 19 
7 4 17 8 8 18 


ORAL EXERCISE. 


44, a. John has 14 marbles and Henry has 4; how many 
marbles have they both ? 

b. Joseph has 19 cents and Harry has 12 cents; how many 
more cents has Joseph than Harry ? 

c. George walked 19 miles and Ned walked 11 miles; how 
much farther did George walk than Ned ? 

d. Albert had 18 apples and gave away 12; how many apples 
had he left ? | 

e. Carrie dressed 16 dolls and sold 11 of them; how many 
were left ? 

f. There are 19 pupils in one class and 15 in another; how 
many more in one class than in the other ? 

g. James started to walk 18 miles; when he had walked 11 
miles how much farther had he to go? 

h. A man has 17 cows and 12 sheep; how many more cows 
has he than sheep ? 

7. Willie has 18 books and Albert has 13; how many more 
books has Wille than Albert ? 

j. George has 17 oranges and 14 peaches; how many more 
oranges than peaches has he’? 


78 FIRST STEPS IN ARITHMETIC. 


i. In an orchard are 12 pear trees and 7 apple trees; how 
many of both are there? 

7. In a dish are 14 red roses and 5 white roses; how many 
roses are in the dish ? 

m. On a table are 11 roses and 7 pinks; how many flowers 
are on the table ? 

Make a number story for each of these: 


12+ 4 11+ 7 19 — 3 19: ——) 16—11 
13th ees epee, (en ie V7 le 
144+ 3 {67a 18: 7% 191115 19 —11 
AD. ORAL AND WRITTEN EXERCISE. 
*0) al *9 #9 ¥0 *] *9 
*2 ¥7 #4 ¥() ¥4 #5, #9 
*] *9 *4 *7 *3 *4 *4 
*] #9 #3 *0 *] *2 #1 
*6 #5, ¥6 *Q ¥7 ¥6 *Q 
#9 *9 *() 4 *2 *] 
5) *7 *6 *5 A. #5 


a. Give sums at sight. 
b. Give sums at sight, substituting 1 for upper *. 
c. Give sums at sight, substituting 1 for lower *. 


e2 


lo 


leon 


a. Subtract, giving remainders at sight. 
6. Subtract, substituting 1 for *. 


Jro oe 


Subtract: 
19 19 
eC 
16 19 
3 2 
18 18 
10 17 
19 18 
15 12 


NUMBERS FROM TEN TO TWENTY. 


vd. 
4 


*9 
= 


* 
a! 


lo 


* 
~l 


| 


*7 
BS 


#8 
Be 


val 
i) 


*6 
AY 


* 
bo oO 


loo 


eo 


*8 
1 


*9 
x 


#3 
8 


*7 
= 


lo A 


loo & 


Inn 


* 
~l 


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bi 


| oo 


*6 


lo 


19 


80) FIRST STEPS IN ‘ARITHMETIC. 


SECTION VIII. 
INCHES AND SQUARE INCHES. 


4G. This line is an inch long. Draw a line an inch long (or 
lay a one-inch stick). Draw one two inches long. How much 
longer is the two-inch line than the one-inch line? How many 
times as long is it? How many one-inch sticks are needed to 
make a two-inch line? What part of the two-inch line is the 
same length as the one-inch linet | 

Make a three-inch line. How much longer is it than the one 
inch line? than the two-inch line ? 

What part of the three-inch line is the same length as the one- 
inch line? What part of the three-inch line 1s the same length as 
the two-inch line ? 

Make a four-inch line. How much longer is it than the one- 
inch line? than the two-inch line? than the three-inch line? 
How many two-inch lines will make a four-inch line? What 
part of the four-inch line 1s the same length as the one-inch line ? 
What part is the same length as the two-inch line? What part 
is the same length as the three-inch line? 


Make a line five inches long. Divide it into five equal parts. 
How long is each part ? 


Tf anything is divided. into five equal parts, each part is called one 

How many fifths in the whole? If one fifth is taken away, 
what part of the line is left? UH two fifths are taken away, 
what part of the line is left?~ If three fifths are taken away, 
what part is left ? If four fifths are taken away, what part is left ? 


INCHES AND SQUARE INCHES. 81 


What is one fifth of five inches? Three fifths of five inches? 
Two fifths of five inches? Four fifths of five mches? How 
much longer is the five-inch line than the one-inch Ime? than 
the four-inch line? than the three-inch line? than the two-inch 
line ? F 


47. Make a line six inches long. How many one-inch Imes 
does it take to make it? How many two-inch lines? How 
many three-inch lines? How much longer is it than a one-inch 
line? than a five-inch line? than a three-inch lme? than a two- 
inch line? than a four-inch line ? 

Divide it into six equal parts? How long is each part ? 

If anything ts divided into six equal parts, each part is called one 
sixth, 

How many sixths in the whole? If one sixth of the line 1s 
taken away, what part of the line is left? If two sixths are 
taken away, what part is left? If five sixths are taken away, 
what part is left? If three sixths are taken away, what part is 
left? If four sixths are taken away, what part of the line is 
left ? 

Divide the line into two equal parts. What is each part called ? 
How many sixths are equal to one half? 

Divide the line into three equal parts. What is each part 
called? How many sixths are equal to one third? What is one 
sixth of six inches? What is one third of six ches? What is 
one half of six inches? How much longer is the six-inch line 
than the one-inch line? than the four-inch line? than the two- 
inch line? than the five-inch line? than the three-inch line ? 

Make a seven-inch line. How much longer is it than the one- 


inch line? than the six-inch line? than the four-inch line? than 
6 


82 FIRST STEPS IN ARITHMETIC. 


the two-inch line? than the five-inch line? than the three-inch 
line ? 

How many times will it contain the one-inch line? the two- 
inch line? the three-inch line? the four-inch line? the five-inch 
line? the six-inch line ? 


Divide it into seven equal parts. Hach part is called one 
seventh. 


What is one seventh of seven inches? If one seventh of the 
line is taken away, what part of the line is left? If three 
sevenths of it are taken away, what part is left? If six sevenths 
of it are taken away, what part is left? If four sevenths of it 
are taken away, what part is left? If five sevenths of it are 
taken away, what part is left? If two sevenths of it are taken 
away, what part is leit ? 


Make an eight-inch line. How much longer is it than the 
one-inch line? than the three-inch line? than the seven-inch line ? 
than the five-inch line? than the two-inch line? than the six- 
inch line? than the four-inch line ? 


Divide it into @ight equal parts. Each part is called one 
eighth. What is one eighth of eight inches? If one eighth of 
the line is taken away, what part of the line will be left? If six 
eighths are taken away, what part will be left? If four eighths 
are taken away, what part will be left? If seven eighths are 
taken away, what part will be left? If five eighths are taken 
away, what part will be left? If two eighths of the line is taken 
away, what part will be left? If three eighths of the lme is 
taken away, what part of it will be left ? 


How many times will it contain the one-inch line? the two- 


inch line? the three-inch line? the four-inch line? the five-inch 
line? the six-inch line? the seven-inch line? 


INCHES AND SQUARE INCHES. 83 


Divide it into two equal parts. What is each part called ? 
How many eighths equal one half? Divide it into fourths. How 
many eighths equal one fourth ? 


48. Make a line nine inches long. How much longer is it 
than the one-inch line? than the seven-inch line? than the six- 
inch line? than the four-inch line? than the five-inch line? than 
the three-inch line? than the two-inch line? than the eight-inch 
line. 


How many times will it contain the one-inch line? the three- 
inch line? the two-inch line? the four-mch hne? the five-inch 
line? the six-inch line? the seven-inch line? the eight-mch 
line? 

Divide it into nine equal parts. Hach part is called one ninth. 
If one ninth of the line is taken away, what part will be left? If 
seven ninths are taken away, what part will be left? If three 
ninths are taken away, what part will be left? If five ninths 
are taken away, what part will be left? If eight ninths are 
taken away, what part will be left? If two ninths are taken 
away, what part will be left? If four ninths are taken away, 


what part will be left? If six nmths are taken away, what part 
will be left ? 


Divide the line into three equal parts. What is each part 
called? One third is equal to how many ninths? Two thirds 
equals how many ninths? 


49. Make a line ten inches long. How much longer 1s it 
than the one-inch line? than the five-inch line? than the seven- 
inch line? than the four-inch line? than the six-inch line? than 
the nine-inch line? than the three-inch lme? than the eight-mch 
line? than the two-inch line? 


34 FIRST STEPS IN ARITHMETIC. 


How many times will it contain the one-inch line? the two- 
inch line? the five-inch line? the seven-inch line? the eight-inch 
line? the three-inch line? the six-inch line? the four-inch Ime? 
the nine-inch line? 

Divide it into ten equal parts. Each part is called one tenth. 


If one tenth of the line is taken away, what part of the line 
will be left? If four tenths are taken away, what part will be 
left? If seven tenths are taken away, what part will be left? 
If three tenths are taken away, what part will be left? If five 
tenths are taken away, what part will be left? If nine tenths 
are taken away, what part will be left? If six tenths are taken 
away, what part will be left? UH four tenths are taken away, 
what part will be left? If eight tenths are taken away, what 
part will be left ? 

Divide it into two equal parts. What is each part called? 
One half equals how many tenths? 

Divide it into five equal parts. What is each part called? 
What is one fifth of ten inches? four fifths of ten inches? two 
fifths of ten inches? three fifths of ten inches? One fifth equals 
how many tenths? 


50. How long is each side of this square? A square whose 
sides are each one inch long is called a square inch. 


INCHES AND SQUARE INCHES. 85 


Make (draw, cut, or lay sticks or tablets) an oblong two 
inches long and one inch wide. Divide the long sides into two 
equal parts and connect the points. How many square inches in 
the oblong? What part of the oblong is one square inch? The 
oblong is how many times as large as the square ? 


Make an oblong four inches long and one inch wide. Divide 
it into square inches. How many square inches in the oblong? 
What part of the oblong is one square inch? The oblong is how 
many times as large as one square inch ? as two square inches ? 
Two square inches are what part of the oblong? Three square 
inches are what part of the oblong ? 


Make a square whose sides shall each be two inches long. 
Divide it into square inches. How many rows of square inches 
in the square? How many square inches in each row? How 
many are two times two square inches? How many square 
inches in the square? How many square inches in three fourths 
of the square? in one half of it? 


Make an oblong five inches long and one inch wide. Divide 
it into square inches. How many square inches in the oblong? 
One square inch is what part of the oblong? four square inches ? 
two square inches? three square inches? 


Make an oblong three inches long and two inches wide. 
Divide it into square inches. How many square inches in one 
row across the oblong? How many rows are there across the 
oblong? How many are two times three square inches? Into 
how many parts does the line across the oblong divide it? What 
is each part called? What is one half of six square inches? 
How many times are three square inches contained in six square 
inches? Into how many parts do the lines up and down the 


86 FIRST STEPS IN ARITHMETIC. 


oblong divide it? What is each part called? How many 
square inches in each third of the oblong? How many are three 
times two square inches? How many times are two square inches 
contained in six square inches? What is one third of six? two 
thirds of six? What part of six inches is two inches? three 
inches? four inches ? 


WRITTEN EXERCISE. 


De eer DEX pee oh GE Gr 
Bs Soe? Wot Aer of 6 = ? 


of 4=? 
Ofaol— ae 


Co bo 
cso HBIOO 


Make squares or oblongs containing one square inch; two 
square inches; three square inches; four square inches; five 
square inches; six square inches, 


51. Make an oblong seven inches long and one inch wide. 
Divide it into square inches. One square inch is what part of it? 
How many times as large as a square inch is it? 

Make an oblong four inches long and two inches wide. Divide 
it into square inches. How many square inches are In one row 
across the oblong? How many such rows? How many are two 
times four square inches? How many times are four square 
inches contained in eight square inches? What is one half of 
eight square inches ? 

How many square inches are in each row up and down the 
oblong? How many such rows are there? How many are four 
times two square inches? How many times are two square 
inches contained in eight square inches? What is one fourth of 
eight square inches? three fourths of eight square inches ? 


Make a square whose sides are each three inches long. Divide 
it into square inches. How many square inches are in each row? 


INCHES AND SQUARE INCHES. ST 


How many such rows are there? How many are three times 
three square inches? How many times are three square inches 
contained in nine square inches? What is one third of nine 
square inches? What are two thirds of nime square inches? 
One square inch is what part of nine square inches? Three 
square inches are what part of nine square inches? Six square 
inches are what part of nme square inches ? 

Make an oblong five inches long and two inches wide. Divide 
it into square inches. How many square inches are in each long 
row ? How many long rows are there? How many are two times 
five square inches? How many times are five square inches con- 
tained in ten square inches? What is one half of ten square 
inches? How many square inches are in each short row? How 
many short rows are there? What are five times two square 
inches? How many times are two square inches contained in 
ten square inches? Two square inches is what part of ten 
square inches? What are two fifths of ten square inches? What 
are three fifths of ten square inches? What are four fifths of 
ten square inches ? 


WRITTEN EXERCISE. 


rece ett (ite, a) ee 10 = 2.—— 2 2a 8) A 
RAS Een Na VN) ee eed > a) a 
ox Oo =.? 8§—-2=/? 1 of Qo=sF As) Ga! Bet 
ye ea 9+3=? Ol LU eer of 10=°? 
ee mee 2 10+5=? oes late Raed 7 Ol LU 
Be 8+4=? Sts 1 Ol Si7 


Make oblongs and squares containing seven square inches; 
eight square inches; nine square inches; ten square inches. 


88 FIRST STEPS IN ARITHMETIC. 


SECTION IX. 


ELEVEN. 


52. a. How many are nine and two? 
b. How many are eight and three? 
c. How many are seven and four? 
d. How many are six and five ? 

e. How many are two and nine? 

f. How many are three and eight? 
g. How many are four and seven * 
h. Wow many are five and six ? 

i. Nine and how many are eleven? 
j. Hight and how many are eleven? 
k. Seven and how many are eleven? 
]. Six and how many are eleven ? 
m. Two and how many are eleven ? 
n. Three and how many are eleven? 
o. Four and how many are eleven ? 
p. Five and how many are eleven ? 


qg. Beginning with the tablet at the left, add the dots in each 
one, beginning at the top. 


ELEVEN. 89 


r. Beginning with the tablet at the right, add the dots in eack 
one, beginning at the top. 

s. Beginning at the left, add the dots in each tablet, beginning 
at the bottom. 

t. Beginning at the right, add the dots in each tablet, begin- 
ning at the bottom. 

u. Beginning at the left, take away the upper groups. (Re- 
cite “ Eleven less nine is two.’”’) 

v. Beginning at the right, take away the upper groups. 

w. Beginning at the left, take away the lower groups. 7 

z. Beginning at the right, take away the lower groups. 

(Close the books.) 

Can you think of the groups in the same order ? 

Begin at the left at the top and try to tell them. 

What is the one at the right? at the left? next to the right ? 
next to the left? 

Make a number story about nine and two; about eight and 
three; about six and five; about seven and four. 

Make a number story about eleven, taking away three; tak- 
ing away seven; taking away nine; taking away six; taking 
away eight; taking away four; taking away two; taking away 
five. 

53. a. A man has eight sheep in one field and three in 
another; how many has he in both fields ¢ 

b. There are seven horses in the barn and four in a lot; how 
many are in both places ? 


c. Jennie had eleven cents and spent three; how many had 
she left ? 


90 FIRST STEPS cIN: ARITHMETIC. 


d. George had eleven cows and sold seven; how many had he 
left ? 


e. Henry had eleven apples and gave away five; how many 
had he left ? 
— f, Willie has nine marbles and Jimmie has two; how many 
have they both ? 

g. Lucy has eleven cents and Carrie has five; how many 
more has Lucy than Carrie? 

h. Abby has six dolls, and Hattie has five; how many have 
they both ? 

i. Mary is eleven years old and Jennie is six years old; how 
much older is Mary than Jennie ? 

jy. Mary is eleven years old and Susie is eight years old ; how > 
much older is Mary than Susie ? 

j:. Carrie is nine years old; in how many years will she be 
eleven ? 

/. Henry has eight dollars ; he wants to buy a chair which 
costs eleven dollars. _How much more money does he need ? 

m. George walked eleven miles and Henry walked seven 
miles; how much farther did George walk than Henry ? 

n. A man has eleven hours’ work to do; how many hours 
must he still work after working nine hours? 


o. John had eleven marbles and lost two; how many had he 
left ? 


p. There are four girls and sevén boys in a class; how many 
children are in the class? 


g. How much longer is an eleven-inch stick than a nine-inch 
stick ? than a two-inch stick ? 


ELEVEN. 91 
r. How much longer is an eleven-inch stick than an eight- 
inch stick ? than a three-inch stick ? 
s. How much longer is an eleven-inch stick than a six-inch 
stick ? than a five-inch stick? 
¢. How much longer is an eleven-inch stick than a seven-inch 
stick? than a four-inch stick ? 7 


U@ 6+?=11 fee a ae 4+ ?=11 es ge —— on | 
i ie a iy or 7+ ?sll 

vw 11—3 =? 11—9=? 11—V7=°? ll —2= 7 
li —5 =? 1l1—4=? 1l1—6=? 


54. Add: 


a b c d e ap g 
4 5 3 2 5 4 2 
5) 2 2 3 3) 3 7 
3 a Ue + 3 4 a 
h a J k Y m n 
3 4) 1 1 2 1 2 
6 1 6 3 t 2 3 
2 mi a 5 8 5 

7) P q r s t u 
1 2 2 1 2 it 2 
3 3 5) 7 1 5) 4 
9) 6 + 2 33 oO = 


|\ranrwe 
Jn ae & 
lo ww 8 
Jn ore 
[ro eo & & 


FIRST STEPS IN ARITHMETIC. 


Subtract at sight : 


11 
4 


= 


11 11 uy 11 11 ina 11 11 
1 8 2 6 9 7 3 vo 


CET aes 


55. Add the dots on these tablets, beginning at the left. 
How many are two twos? three twos? five twos? four twos ? 


Five twos and one more ? 


Hight is how many twos? 
Four? Six? Ten? Eleven? 


a. 


At two cents apiece, how many tops can be bought for 


eleven cents ? 


b. 


C. 


How many quarts of milk are eleven pints ? 
How many two-inch sticks can be cut from a stick eleven 


inches long ? 


d. 


How many chairs at two dollars apiece can be bought for 


eleven dollars ? 


€. 


# 


Eight pints are how many quarts? 
How many tops at two cents apiece can be bought for eight 


cents? for nine? for ten? for eleven ? 


9: 
h. 


ie 


ip 
k. 
i 


How many twos in eleven ? 

Eleven divided by two is how many ? 
Six divided by two? 

Eight divided by two ? 

Seven divided by two ? 

Five divided by two? 


ELEVEN. 93 


m. Nine divided by two? 
n. Four divided by two? 
o. Ten divided by two? 
p. Three divided by two ? 


WRITTEN EXERCISE. 


a. In seven pints there qts. and pt. 


two-dollar chairs and 


b. For eleven dollars I can buy 
left. 


c. In ten pints there are 


have 


qts. 


d. For nine cents I can buy two-cent tops and have 


left. 
e. Write from / to p in lesson above in figures. 


Eee ae 


56. Add these dots, beginning at the left. 
How many are two threes? three threes? three threes and 
two more? Eleven is how many threes? Nine? Six? 


How many are two threes and one more? Two threes and 
two more? Three and one? Three and two? Four is how 
many threes? Seven? Five? Eight? 

Draw a line one foot long. Draw a line three feet long. A 
line three feet long is one yard long. Draw a line two feet long. 
Draw one four feet long. How many yards long is it? Two 
yards are how many feet? ‘Two yards and two feet are how 
many feet? Three yards are how many feet? Three yards and 
two feet are how many feet? 


94 - FIRST STEPS) (NGARTT aM Eda 


a. At three cents apiece, how many slates can be bought for 
eleven cents ? 

>. At three dollars each, how many chairs can be bought for 
eleven dollars ? 

ce. How many three-inch sticks can be cut from a stick eleven 
inches long ? 

d. How many yard sticks can be cut from a stick eleven feet 
long? 

e. How many triangles can you lay with six sticks? 

f. How many hours would it take to walk nine miles if you 
walk three miles an hour ? 

g. How many threes in eleven ? 

h. Eleven divided by three is how many? 

i. Nine divided by three ? 

7. Seven divided by three? 

k. Ten divided by three? 

i. Five divided by three ? 

m. Hight divided by three? 

n. Six divided by three ? 

o. Four divided by three ? 


WRITTEN EXERCISE. 


a. In six feet there are yards. 
b. In eleven feet there are —— yards and feet. 
c. Three triangles have sides. 


three cent tops and have 


d. For eleven cents I can buy 
cents left. 


ELEVEN. 95 


e. For eleven dollars I can buy three-dollar chairs and 
dollars left. 

jf. From an eleven-inch stick I can cut 
and have one inch stick left. 


g. Write from / to o in this lesson in figures. 


bacarl gal 


57. Add these dots b eginning at the left. How many are 
two tours? ‘Two fours and three more ? 


pede) | * 


Add these dots, beginning at the left. How many are two fives 
and one more? How many fours are there in eleven? How 
many fives ? : 


have 


three-inch sticks 


. At four cents each, how many plates can you buy for eleven 
Ie ? 


6. How many gallons are eleven quarts ? 


e. At five dollars each, how many tables can you buy for 
eleven dollars ? 


d. How many bushels are eleven pecks ? 


e. George bought two tops for four cents each and a book for 
three cents; what did they all cost? 


J. A man bought two chairs for five dollars each and a stand 
for one dollar; what did they all cost ? 


96 FIRST STEPS IN ARITHMETIC. 


g. Eleven divided by four is how many ? 
h. Eleven divided by five ? 

7. Nine divided by four? 

7. Seven divided by four ? 

k. Ten divided by four ? 

7. Six divided by four ? 

m. Kight divided by four ? 

n. Five divided by four ? 


ORAL AND WRITTEN EXERCISE. 


a. George bought two pads for five cents each and a pencil for 
one cent. He spent cents. 


b. Two bushels and three pecks are pecks. 


four-dollar chairs and 


c. For eleven dollars I can buy 
have dollars left 


d. For eleven cents I can buy 
left. 


e. Write from / to n in this lesson in figures. 


five-cent slates and have 


Find out these for yourselves and make number stories to fit 
them: 


ig beceay ee iia a ete arena a Ra Deeg 19 re eh eee 


TWELVE. OT 


SECTION X. 


TWELVE. 


58. a. How many are nine and three? 
6b. How many are eight and four? 
c. How many are seven and five ? 
d. How many are six and six ? 
e. How many are three and nine? 
jf. How many are four and eight ? 
g. How many are five and seven ? 
h. Nine and how many are twelve ? 
a. Eight and how many are twelve ? 
j. Seven and how many are twelve? 
k. Six and how many are twelve ? 
/. Three and how many are twelve ? 
m. Four and how many are twelve ? 
n. Five and how many are twelve ? 
o. Beginning with the tablet at the left, add the dots in each 
one, beginning at the top. 
p. Beginning with the tablet at the right, add the dots, begin- 
ning at the top. 


q. Beginning with the tablet at the left, add the dots, begin- 
ning at the bottom. 


98 FIRST STEPS IN ARITHMETIC. 


ry. Beginning with the tablet at the right, add the dots, begin- 
ning at the bottom. 


S. Beginning with the tablet at the left, take away the upper 
oroups. 

t. Beginning at the right, take away the lower groups. 

u. Beginning at the right, take away the upper groups. 

v. Beginning at the left, take away the lower groups. 

(Close the books.) 

Think of the groups in the order in which they are given in 

the book. 


What is the tablet at the left? at the right? next to the left ? 
next to the right? 

Make a number story about nine and three; about seven and 
five; about six and six; about eight and four. 

Make a number story about twelve, taking away six; taking 
away eight; taking away three; taking away five; taking away 
seven; taking away four; taking away nine. 


59. «a. Jessie has nine roses and three pinks; how many 
flowers has she? 


b. There are seven boys and five girls in a class; how many 
children are in the class ? 


-e. George had twelve marbles and lost four of them; how 
many had he left? 
d. A man had twelve sheep and sold six of them; how many 
had he left ? | 


e. John is twelve years old and Mary is eight years old; how 
much older is John than Mary? 


TWELVE. ¥9 


f. Henry is nine years old; in how many years will he be 
twelve ? 

g. Susie wrote twelve words and Lucy wrote seven; how 
many more words did Susie write than Lucy ? 

h. Mary read eight books in one year, and Carrie read four 
books; how many books did they both read ? 

i. Carrie wrote six words in the morning and six words in the 
afternoon; how many words did she write in all? 

7. John had twelve cents and spent five cents for a slate ; how 
much had he left ? 

i. James had seven peaches and a man gave him five more ; 
how many peaches had he then ? 

1. There are nine trees in one yard and three trees in the next 
yard; how many trees are there in both yards ? 

m. George earned eight cents and Henry earned four cents; 
how many cents did they both earn ? 

n. Willie is six years old; in how many years will he be 
twelve ? 

0. How much longer is a twelve-inch line than a three-inch 
line ? than a nine-inch line? 

-p. How much longer is a twelve-inch line than a seven-inch 

line? than a five-inch line ? 

g. How much longer is a twelve-inch line than an eight-inch 
line? than a four-inch line ? | 

r. How much longer is a twelve-inch line than a six-inch line ? 


a ee Ey a es Pee os 12—3=? 127 tte 


12-9 => 12—5=? se? 


FIRST STEPS IN ARITHMETIC. 


100 


60. Add: 


‘60 


CO 


N 


oD 


te) 


H 


tes) 


co 


“uD 


_ 


| 


<9 | 


Subtract at sight 


12 


12 


12 


12 


12 


12 


al 


N 


p Yor) 


re 


(o.@) 


oO 


12 


12 


12 


12 


ae 


=| 


| 


WRITTEN EXERCISE. 


sH 


oO 


© 


CO 


ite) 


=| 


fan) 


TWELVE. 101 


a. Write table of additions, beginning with the upper number. 
6. Write table of additions, beginning with the lower number. 
ce. Write table of subtractions, taking away the upper number. 
d. Write table of subtractions, taking away the lower number. 
e. Write a number story about eight and four. 

J. Write a number story about six and five. 

g. Write a number story about eleven less three. 

h. Write a number story about twelve less seven. 


61. Add the dots on these tablets, beginning at the left. 
How many are two twos? four twos? three twos? five twos? 
six twos ? 
Twelve is how many twos? Eight? Six? Four? Ten? 
Nine? Three? Seven? Five? 
a. How many chairs at two dollars apiece can be bought for 
twelve dollars ? 
6. Twelve pints are how many quarts ? 
e. How many two-inch sticks can be cut from a stick twelve 
inches long ? 
d. How many tops at two cents apiece can be bought for 
twelve cents? for ten cents ? 
e. How many twos in twelve? 
J. Twelve divided by two is how many ? 
g. Three divided by two is how many ? 
h. Ten divided by two is how many ? 


102 FIRST STEPS UN ARITHMETIC 


7. Four divided by two is how many ? 

j. Nine divided by two is how many ? 

k. Five divided by two is how many ? 

/. Seven divided by two is how many ? 

m. Kight divided by two is how many? 

n. Six divided by two is how many ? 

o. Kleven divided by two is how many ? 
With books closed, add by twos to twelve. 


WRITTEN EXERCISE. 


a. Twelve pints are quarts. 


6. For twelve cents I can buy 


two-cent tops. 


two-dollar chairs. 
d. Write from f to o in this lesson in figures. 


62. Add these dots, beginning at the left. How many threes 
are there? How many are four threes? two threes? three 
threes? How many threes in twelve? in nine? in six? 


c. For twelve dollars I can buy 


a. At three cents each, what is the cost of four tops? 

b. At three dollars each, what is the cost of four chairs ? 

c. At three cents apiece, how many slates can be bought for 
twelve cents ? 


d. At three dollars each, how many chairs can be bought for 
twelve dollars ? 


TWELVE. 103 


e. How many triangles can be laid with twelve sticks ? 


jf. How many three-inch sticks can be cut from a stick twelve 
inches long ? 


g. How long is a foot? 
h. How long is a yard? 
gs ) 


7. How many yard sticks can be cut from a stick twelve feet 
long? 


j. Twelve divided by three is how many ? 

k. Nine divided by three is how many ? 

/. Six divided by three is how many ? 

m. Kight divided by three is how many ? 

n. Ten divided by three is how many ? 

o. Seven divided by three is how many ? 

p. Eleven divided by three is how many ? 

q. Five divided by three is how many ? 

7, With books closed, add by threes to twelve. 


WRITTEN EXERCISE. 


a. For twelve dollars IT can buy three-dollar hats. 

6. For nine cents I can buy —— three-cent tops. 

e. For eleven cents I can buy -—— three-cent tops and have 
left. 


d. From a twelve-inch stick I can cut three-inch sticks. 


é. From a twelve-foot stick 


yard sticks can be cut. 


f. Write from 7 to g im this lesson in figures. 


104 FIRST STEPS IN ARITHMETIC. 


63. a. How many are two fours? three fours ? 

b. How many are two fives? two fives and two more ? 
e. Hight is how many fours ? 

d. Twelve is how many fours ? 

e. Ten is how many fives? 

f. Eleven is how many fives ? 

g. Twelve is how many fives ? 


h. How many bananas at four cents each can be bought for 
eight cents? for twelve cents ? 


2. How many pecks in two bushels? in three bushels ? 
7. How many quarts in two gallons? in three gallons ? 
k. Kight pecks are how many bushels ? 

7. Twelve pecks are how many bushels? 

m. Twelve quarts are how many gallons ? 

n. Kight quarts are how many gallons ? 


o. How many tables for five dollars each can be bought for 
twelve dollars ? 


p. How many books at five cents apiece can be bought for 
twelve cents ? 


g. Twelve divided by four is how many ? 
r. Twelve divided by five is how many ? 


WRITTEN EXERCISE. 


a. Eight quarts are gallons. 


b. Twelve quarts are gallons. 


TWELVE. 105 


ce. Eight pecks are bushels. 


d. ‘Twelve pecks are bushels. 
rR Nee: Bea rk Agee 8+4=? 12+4=? 
10+5=? 12+5=? 
Find these out for yourself and make number stories for them : 
12+ 6=? 12+7=? 12+8=? 12+9=? 
12+10=? 
WRITTEN EXERCISE. 


a. For twelve dollars I can buy six-dollar chairs. 


6b. How many seven-inch sticks can I cut from a twelve-inch 
stick? What will be left ? 


c. How many eight-cent slates can you buy for twelve cents ? 
What will be left ? 


d. How many nine-foot sticks can be cut from a twelve-foot 
stick? What will be left ? 


e. How many ten-cent pictures can you buy for twelve cents ? 
What will be left ? 


12 —3 = 7 12; 4:7 12—- 9=? 
12—-2=°? 12 (= 2 aes fi — es 
12—+-6=? 12 10 7 12—10=? 


64. Draw a line twelve inches long. Divide it into two 
equal parts. 


a. What is the name of each part ? 
6. How many inches in each part ? 


ce. How many inches in half a foot ? 


106 


FIRST STEPS IN ARITHMETIC. 


d. What is one half of twelve? Divide each half of the line 
into two equal parts. 


a 
ve 
UE 


Into how many parts is the line divided ? 
What is the name of each part ? 
What is 4 of 4? 


h. How many inches are in each part ? 


i. 
de 
k. 


l. 


How many inches are in + of a foot? 

What is $ of 12? 

One half of twelve equals how many fourths of twelve ? 
What is 2 of 12? 


m. What is 3 of 12? 


I. 


Draw another line twelve inches long. Divide it mto three 


equal parts. What is each part called? 


0. 
D: 
q. 
. What is $ of 12? 2 of 12? 


. Divide each third into two equal parts. 


How many inches are in each part ? 
How many inches are in } of a foot? 


How many inches are in 2 of a foot ? 


. Into how many parts is the line divided ? 
. What is the name of each part ? 
. What is 4 of 3? 


How many inches are in } of a foot? 


. What is 4 of 12? 


of a foot is equal to how many sixths of a foot? 


1 
3 
. 1 of a foot is equal to how many sixths of a foot? 


TWELVE. 107 


ORAL AND WRITTEN EXERCISE. 


$o0f 12> 7% 3 of 12 =? sof 12=? 
tof 12=°? $o0f 12=? aS 6) oo be ed 
goof 12=? eae jit Ue ear 
tof 12=? SOle cies at tof 4=°5 

$=% t$=¢ Zof 4=? 


65. a. Carrie had 12 cents and spent } of them; how many 
did she spend ? 


b. Ilow many did she have left ? 


c. Lucy had 12 apples and gave away + of them; how many 


did she give away ? 


H>|4 


d. How many did she have left ? 


e. Henry had 12 marbles and lost } of them; how many did 
he lose ? 


ft. How many did he have left ? 


g. John had 12 papers and sold 4 of them; how many did he 
sell ? 


h. How many did he have left ? 


7. George had 12 cents and spent 2 of them; how many cents 
did he spend ? 


7. How many did he have left ? 


k. Jennie had 12 yards of cloth; she used 3 of it for a dress 
and + of it for a coat. How many yards did the dress take ? 
/. How many yards did the coat take ? 


m. Twelve is one dozen. How many eggs in half a dozen ? 


WRITTEN EXERCISE. 


Draw pictures of the problems in this lesson. 


108 FIRST STEPS IN ARITHMETIC. 


SECTION XI. 


THIRTEEN. 


66. «a. How many are nine and four? 


6. How many are eight and five ? 
c. How many are seven and six? 
d. How many are four and nine? 
e. How many are five and eight ? 
J. How many are six and seven ? 
g. Nine and how many are thirteen ? 
h. Kight and how many are thirteen? 


Seven and how many are thirteen ? 


=~. 
° 


J. Four and how many are thirteen ? 

k. Five and how many are thirteen ? 

/. Six and how many are thirteen ? 

m. Begmning with the tablet at the left, add the dots in each 
one, beginning at the top. 

n. Beginning with the tablet at the right, add the dots in each 
one, beginning at the top. 


THIRTEEN. 109 


0. Beginning at the left, add the dots im each tablet, beginning 
at the bottom. 


p. Beginning at the right, add the dots in each tablet, begin- 
ning at the bottom. 


wu. Beginning at the left, take away the upper groups. 
Recite “ Thirteen less nine are four.” 
v. Beginning at the right, take away the upper groups. 
w. Beginning at the left, take away the lower groups. 
«. Beginning at the right, take away the lower groups. 
(Close the books.) 
Think of these groups in that same order. What is the one 
at the left? the right? in the middle ? 


Make a number story about the left-hand one, adding the 
numbers. 


Make a number story about the middle one, taking away the 
upper number. 


Make a number story about the right-hand one, taking away 
the lower number. 


What other numbers make thirteen besides these ? 


67. a. George had eight cents and found five cents; how 
much money had he then ? 

6. Carrie had nine books and bought four; how many had 
she ? 

ce. James walked seven miles in the morning and six miles in 
the afternoon; how many miles did he walk ? 


110 FIRST STEPS IN ARITHMETIC. 


d. A man has six cows and seven sheep; how many animals 
has he? 

e. Lucy has five pinks and eight roses; how many flowers has 
she ? 

f. George has four marbles and Henry has nme; how many 
have they both ? 

g. Jessie has nine books; how many must she get to make 
thirteen ? 

h. Carrie has seven dolls; Lucy has enough to make thirteen. 
How many has Lucy? 

i. John is eight years old; in how many years will he be 
thirteen ? 

7. George is ten years old; in how. many years will he be 
thirteen ? 

k. Henry has thirteen marbles and John has seven ; how many 
more marbles has Henry than John? 

l. Joseph walked thirteen miles and Frank walked nine miles ; 
how much farther did Joseph walk than Frank ? 

m. Walter has eight dollars; he wants to buy a table which 
costs thirteen dollars; how much more money does he need to 
buy the table ? 

n. A man had thirteen hours’ work to do; he did seven hours’ 
work one day; how many hours must he work the next day ? 

o. How much longer is a thirteen-inch stick than a nme-inch 
stick? than a four-inch stick ? 

». How much longer is a thirteen-inch stick than an eight- 
inch stick ? than a five-inch stick ? 

g. How much longer is a thirteen-inch stick than a seven- 
inch stick? than a five-inch stick ? 


111 


THIRTEEN. 


Y. 


+ ?= 13 


Ce Poles 


13 — 5 


| 


13 —7 


13 


4+ ?=13 


8+?= 


13 


G4 


t. Add at sight: 


10 


11 


10 


ig! 


12 


10 


nen) 


N 


N 


re 


wu. Subtract at sight: 


18 


12 


13 


13 


12 


11 


N 


N 


rl 


ml 


Ak 


12 


13 


13 


13 


= 


re 


68. Add: 


Yen) 


ot 


to) 


t~ 


t~ 


ue 


D 


N 


Yorn) 


| 


= 


112 FIRST STEPS IN ARITHMETIC. 


i P q r s t u 
i) 8 4 3 8 2 1 
3 3 6 6 4 4 3 
By: 5: 84 es i foe 
v w 2 y z 
4 2 3 1 2 
7 1 3 4 5) 
oils te ag ye 
Subtract at sight: 
13 13 13 13 13 13 
3 8 2 9 
13 13 13 13 13 13 
i) ot 2 10 12 11 


eee 


69. Add these dots, beginning at the left. 

How many are two twos? four twos? three twos? six twos? 
five twos ? | 

Ten is how many twos? Eight? Four? Six? Twelve? 
Seven? Three? Five? Eleven? Thirteen? 

a. How many two-cent tops can you buy for thirteen cents ? 

b. How many two-inch sticks can be cut from a stick thirteen 
inches long ? 


THIRTEEN. 113 


c. How many quart dishes can you fill with thirteen pints of 
milk ? 

d. How many two-dollar books can you buy with thirteen 
dollars ? 

e. Thirteen divided by two is how many ? 

f. Six divided by two is how many ? 

g. Eight divided by two is how many ? 

h. Eleven divided by two is how many ? 

7. Seven divided by two is how many ? 

7. Four divided by two is how many ? 

k. Nine divided by two is how many ? 

i. Five divided by two is how many ? 

m. Twelve divided by two is how many ? 

n. Three divided by two is how many? 

o. Ten divided by two is how many ? 


WRITTEN EXERCISE. 


a. For thirteen cents I can buy 
left. 


b. Write from e to o in this lesson in figures. 


arene Lt 


70. Add these dots, beginning at the left. 


How many are two threes? four threes? three threes ? 
8 


two-cent tops and have 


114 FIRST STEPS IN ARITHMETIC. 

Six is how many threes? Twelve? Nine? Thirteen? 
Eleven? Seven? Ten? KHEight? 

a. How long is a foot ? 

b. How long is a yard ? 


c. How many three-inch sticks can be cut from a stick thir- 
teen inches long ? 


d. How many yard sticks can be cut from a stick thirteen 
feet long ? 


e. How many feet long is a piece of cloth three yards long ? 
f. How many feet long is a pole four yards long? 

g. How many yards long is a rope thirteen feet long ? 

h. Ten feet are how many yards ? 

i. How many three-cent tops can you buy for eight cents ? 


yj. How many three-dollar chairs can you buy for eleven 
dollars ? 


k. Twelve divided by three is how many ? 
1. Nine divided by three is how many ? 

m. Seven divided by three is how many ? 

n. Ten divided by three is how many ? 

o. Six divided by three is how many ? 

p. Hight divided by three is how many ? 

g. Eleven divided by three is how many ? 
7. Thirteen divided by three is how many ? 


s. Five divided by three is how many ? 


THIRTEEN. 115 


WRITTEN EXERCISE, 


a. Thirteen feet are yards and 
b. For thirteen cents I can buy 
have left. 


c. Write from / to s in this lesson in figures. 


three-cent oranges and 


EE Sel ea 


71. a. How many are two fours? three fours? three fours 
and one more ? 


b. How many are two fives? two fives and three more ? 


c. George bought three books for four cents each and a pencil 
for one cent; what did he pay for all? 


d. Henry bought two bananas for five cents each and a glass 
of milk for three cents; what did he pay for all? 


e. Two bushels are how many pecks? 

J. Three bushels are how many pecks ? 

g. Two bushels and one peck are how many pecks ? 
h. Three bushels and one peck are how many pecks? 
2. Hight pecks are how many bushels ? 

j. Twelve pecks are how many bushels ? 

k. Thirteen pecks are how many bushels ? 


1. Ten pecks are how many bushels? 


116 FIRST STEPS IN ARITHMETIC. 


m. How many quarts are there in one gallon? 
n. Seven quarts are how many gallons? 

0. Kleven quarts are how many gallons ? 

p. Thirteen quarts are how many gallons? 


g. How many slates at five cents apiece can be bought for 
thirteen cents ? 


r. How many hats at five dollars each can be bought for thir- 
teen dollars? 


s. How many tops at four cents each can be bought for thir- 
teen cents ? 


t. How many fours in thirteen ? 


wu. How many fives in thirteen ? 


WRITTEN EXERCISE. 


2 xXt4 SP 11+4=? 6+5=? 
Dox 4 anor 8+4=? 102 D740 
9+4=? 6+4=? 1S aoe 
12+4=? Papeete 3" 14 11+5=? 
7+4=? HY eet peat 12+-5=? 
10+4=¥? 7+5=? : 5+4=? 
13+4=? 8+5=? 


72. Find these out for yourselves, and make number stories 
for them : 


13.22 6k 18 ae Bo a ee es re ee ee 


FOURTEEN. 117 


WRITTEN EXERCISE. 


a. For thirteen cents I can buy six-cent slates and have 


left. 


6. For thirteen cents I can buy 
left. 


c. How many eight-inch sticks can be cut from a thirteen- 
inch stick? What will be left ? 


d. How many nine-foot sticks can be cut from a thirteen-foot 
stick? What will be left ? 


e. How many ten-cent pictures can you buy for thirteen cents ? 


What will be left 2 


seven-cent balls and have 


138 —-3=? 13—- 8=? 13,2? = ? 
13+7=? 13+10=? 18 —5 =? 
13+9=? 13+ 4=? 13+6=? 


SECTION XII. 


FOURTEEN. 


73. a. Nine and five are how many ? 
b. Eight and six are how: many ? 

oO 
c. Seven and seven are how many ? 


d. Five and nine are how many ? 


118 FIRST STEPSAN. ARITHMETIC: 


e. Six and eight are how many ? 

jf. Take nine from fourteen; how many are left? 
g. Take six from fourteen; how many are left ? 
h. Take eight from fourteen; how many are left? 
7. Take five from fourteen; how many are left ? 
7. Take seven from fourteen; how many are left? 
k. Five and how many are fourteen ? 

/. Hight and how many are fourteen ? 

m. Six and how many are fourteen ? 

n. Nine and how many are fourteen ? 

o. Seven and how many are fourteen ? 

p. What is one half of fourteen ? 


g. Beginning at the left, add the dots in each tablet, beginning 
with the upper number. 


r. Beginning at the left, add the dots in each tablet, begining 
with the lower number. 


s. Beginning at the left, take away the upper number. 
/. Beginning at the right, take away the lower number. 


u. Make a number story about the left-hand tablet, adding the 
numbers. 


v. Make a number story about the middle one, taking away 


the upper number. 


w. Make a number story about the right-hand one, adding the 
numbers. 


a. Ten and how many are fourteen? Thirteen and how 
many ? 


FOURTEEN. 119 


y. Eleven and how many are fourteen? Twelve and how 
many ? 

z. Fourteen less ten are how many ? less twelve ? less thirteen ? 
less eleven ? 


74. a. Walter has eight books and his sister has six books ; 
how many books have they both ? 

b. Ned had fourteen marbles and lost five marbles; how many 
marbles had he left ? 

c. Jessie has nine roses and five pinks; how many flowers has 
she ? 

d. Lucy is fourteen years old and Mary is eight years old; 
how much older is Lucy than Mary? 

e. Susie is six years old; in how many years will she be 
fourteen ? 

f. George started out to walk fourteen miles; after he has 
walked seven miles, how many more miles has he to walk ? 

g. Henry had eight cents and earned six cents; how much 
money had he then ? 

h. Louis is five years old and Charlie is fourteen years old; 
how much older is Charhe than Louis ? 

7. James is nine years old; in how many years will he be 
fourteen ? 

7. George had fourteen dollars and spent six dollars; how 
much money had he left ? 7 

k, Willie has seven cents; he wants to buy a book that costs 
fourteen cents; how much more money does he need ? 


120 FIRST STEPS IN ARITHMETIC. 


~. How much longer is a fourteen-inch stick than a nine-inch 
stick ? 

m. How much longer is a fourteen-inch stick than a six-inch 
stick ? 

n. How much longer is a fourteen-inch stick than a five-inch 
stick ? 

o. How much longer is a fourteen-inch stick than a seven-inch 
stick ? 

p. How much longer is a fourteen-inch stick than an eight- 
inch stick ? 


Gg. 99 +r = 14 Yr. 14-6=? 
8+?=14 14—9=? 
9+ ?=14 144—7=? 
6+ ?=14 14—5=>? 
(eae — 14:—s =F 
4. O6f 14-9 


¢. Add at sight: 


10 10 12 11 ft 10 11 12 10 13 
4 i! 1 3 


a 
I ro 
| no 
los 
| 


wu. Subtract at sight: 


14 12 13 12 13 14 13 12 13 14 
1 10 1 1 11 11 3 2 


— — — — 


[ no 
l os 


1B ye p14, 11 ae 1 A ee ae 
10 seek oe rie Th i TR 


| no 
— 
bo 


121 


FOURTEEN. 


75. Add: 


oD 


oD 


m 


t~ 


ud 


N 


ue 


of 


oD 


t~ 


N 


= 


H 


sith 


w 


20% 


Subtract : 


14 


14 


14 


14 


14 


14 


14 


r= 


© 


(e @) 


N 


14 


14 


14 


14 


14 


14 


oo 


| 


or) 


oa 


“wD 


122 FIRST SLEEPS *HN: Alf lTAuETIC 


(LST Sea 
abalstecemleme ee 
ee 


76. a. Add twos to fourteen. 
b. How many twos in fourteen ? 


c. How many two-cent tops can be bought for fourteen cents ? 

d. To how many people can you give fourteen oranges if you 
sive two oranges to each person ? 

e. Add threes to fourteen. 

jf. Fourteen is how many threes ? 

g. How many three-cent slates can be bought for fourteen 
cents ? 

h. To how many people can you give fourteen apples if you 
give three to each person? How many apples will you have 
left ? 

2. Add fours to fourteen. 

j. Fourteen is how many fours ? 

k. Fourteen pecks are how many bushels ? 

7, Fourteen quarts are how many gallons ? 

m. Add fives to fourteen. 

n. Fourteen is how many fives? 


FOURTEEN. 128 


o. At five cents each, how many blank books can you buy for 
fourteen cents ? 


P 


. Add sixes to fourteen. 


g. Fourteen is how many sixes ? 


Ae 


Ss. 


t. 


Add sevens to fourteen. 
Fourteen is how many sevens ? 


How many days are there in two weeks ? 


Ww 14+2=? beer aan € 
4+3=? AD ee as” f 
14+4=>? ra af Rem 
14+-5=? Rute ae 
144+6=? Py ih ie Hy 
14+-7=? TS el 


77. Cut apiece of paper or a string fourteen inches long. 
Mark it in inches. 


a 


. If you cut it into inch pieces, how many pieces would you 


have ? 


b. 
G; 


d. 


How many two-inch pieces would it cut into? 
How many three-inch pieces would it cut into? 
How many four-inch pieces would it cut into ? 
How many five-inch pieces would it cut into? 
How many six-inch pieces would it cut into? 

. How many seven-inch pieces would it cut into? 


. If you cut off an eight-inch piece, what would be left ? 


Fourteen divided by eight is how many ? 


124 FIRST STEPS IN ARITHMETIC. 


j. Tf you cut off a nine-inch piece, what would be left ? 

k. Fourteen divided by nine is how many ? 

7. If you cut off a ten-inch piece, what would be left ? 

m. Fourteen divided by ten is how many ? 

n. How many two-foot sticks would a fourteen-foot stick cut 
into ? 

o. How many yard sticks would a fourteen-foot stick cut 
into ? 


Draw an oblong seven inches long and two inches wide. 
Divide it into square inches. 


p. How many square inches are in each of the long rows? 
qg. How many long rows are there ? 

7. How many square inches in the oblong ? 

s. How many are two times seven ? 

t. One half of fourteen is how many? 

uw. How many square inches in each of the short rows? 

v. How many short rows are there? 


w. If anything is divided into seven equal parts, what is each 
part called ? 


z. What 1s one seventh of fourteen ? 


y. George had fourteen cents and spent one seventh of it; 
how much money did he spend? 


z. Carrie had fourteen pieces of candy and gave one half of 
them to her sister; how many did she give her sister ? 


(Jt 


FOURTEEN. 12. 


WRITTEN EXERCISE. 


a. A fourteen-inch stick will make two-inch sticks. 


6. Fourteen quarts of milk will fill gallon cans, and 


leave quarts. 


c. An oblong seven inches long and two inches wide contains 
square inches. 


d. A fourteen-foot stick will make yard sticks, and leave 


a stick feet long. 


bushel baskets and 


e. Fourteen pecks of apples will fill 
leave pecks. 


f. Fourteen cents are equal to five-cent pieces and 
cents. 


six-dollar chairs and 


g. For fourteen dollars I can buy 


have dollars left. 
h 4x8=? 2x6=? 5s he 
yh ae eel 3x4=? 
tilde 8? 14=9=7 10a? 
140-2 B92? jos 5 2 14+ 6=? 


126 FIRST STEPS IN ARITHMETIC. 


SECTION XIII. 


FIFTEEN. 
78. Add at sight: 
11 14 LZ ike 
4 1 2 yy 
Subtract at sight : 
15 15 15 15 15 5 15 15 
il 12 11 3 5 4 lz} 


a. How many are ten and five? 

b. Nine and how many are fifteen ? 

c. Six and how many are fifteen ? 

d. Hight and how many are fifteen ? 

. Take six from fifteen; how many are left ? 


€ 

f. Take eight from fifteen; how many are left ? 
g. Take nine from fifteen; how many are left ? 
h 


. Take seven from fifteen; how many are left ? 


FIFTEEN. 127 


7. Beginning at the left, add the dots in each tablet, beginning 
with the upper number. 

j. Begmning at the left, add the dots in each tablet, beginning 
with the lower number. 

k. Beginning at the left, take away the upper number. 

1. Beginning at the right, take away the lower number. 

m. Make a number story about the left-hand tablet, adding 
the numbers. 

n. Make a number story about the right-hand tablet, adding 
the numbers. 

o. Make a number story about the left-hand tablet, taking 
away the upper number. 

p. Make a number story about the right-hand tablet, taking 
away the wpper number. 

g. Make a number story about the left-hand tablet, taking 
away the lower number. 

vr. Make a number story about the right-hand tablet, taking 
away the lower number. 


79, a. Carrie has eight books and Sarah has seven; how 
many books have they both? 

b. John had fifteen apples and gave away six; how many 
apples has he left? 

e. George is eight years old; in how many years will he be 
fifteen ? 

d. Henry rode nine miles on his bicycle in one hour and six 
miles the next hour; how many miles did he ride in two hours? 


128 FIRST STEPS IN ARITHMETIC. 


e. Lucy is seven years old and Fannie is fifteen years old; 
how much older is Fannie than Lucy ? 


f. Susie had fifteen flowers and gave away nine; how many 
flowers had she left ? 


g. There are six boys and nine girls in a class; how many 
children in the class ? 


h. There are seven sheep and eight cows in a field ; how many 
animals in the field ? 


i. How much longer is a fifteen-foot pole than an eight-foot 
pole ? 


j. How much longer isa fifteen-foot pole than a six-foot pole? 
k. How much longer is a fifteen-foot pole than a nine-foot 
pole ? 


i. How much longer is a fifteen-foot pole than a seven-foot 
pole ? 


Tweet blo 15—8=? 
oe Se tees BS, 15—6=Ff 
94+ ?=15 Li iet 
ieee — Lo 15 —7=? 


n. Subtract at sight : 


15 15 15 15 15 15 15 
Lime ee ee 2 
1 15 15 15 15 15 15 
10 4 14 A 12 8 5 


FIFTEEN. 129 


SO. Add these examples: 


a b c d e ‘ns g 
8 1 7 ) 2 9) 7 
Ley 2 2 5 1 1 2 
i” > a Stipe AD 2 Ge ee 
h a J k l m n 
9 6 8 7 D 4 7 
1 3 1 4 5) 4 4 
DE ree yh Fe 2 
oO Pp q r $s t u 
6 8 8 8 4 9 6 
3 3 2 1 6 4 2 
DEMEEO ieee e Po 8 LY ne 
v w x y 
3 3 4 9) 
8 7 6 5 
5 Cig Salat) 


WRITTEN EXERCISE. 


a. George has one marble, Henry has three marbles, and John 
has eight marbles. They all have marbles. 


b. John spent eight cents for a book, two cents for a pencil, 


and one cent for a rubber. They all cost cents. 
9 


130 FIRST STEPSZIN ARITHMETIC. 


c. George walked four miles one day, two miles the next day, 
and nine miles the next day. In the three days he walked 


miiles. 


d. Henry sold four- books one day, three books the next day, 


books. 


and eight books the next day. In all he sold 


z 
ro} te 


Sl. a. Add twos to fifteen. 
4. Fifteen is how many twos? 


ce. How many two-cent apples can be bought for fifteen cents ? 

d. How many quart cans can you fill with fifteen pints of 
milk ? | = 

e. Add threes to fifteen. 

f. Fifteen is how many threes ? 

g. How many plates would be needed to hold fifteen apples if 
three apples were put on each plate ? 

h. Add fours to fifteen. 

7. Fifteen is how many fours ? 


FIFTEEN. 131 


j. At four cents each, how many bananas can you buy for 
fifteen cents ? 


k. Add fives to fifteen. 
7. Fifteen is how many fives? 


m. If five people can be seated on one bench, how many 
benches would be needed to seat fifteen people ? 


n. Add sixes to fifteen. 

o. Fifteen is how many sixes ? 

p. At six cents each, how many boxes can be bought for fif- 
teen cents ? 

g. Add sevens to fifteen. 

r. Fifteen is how many sevens? 

s. At seven cents each, how many slates can be bought for 
fifteen cents ? 


AALS By ten’ Fe UP1b SQ? 
5xX3=? 15 = 3 =-? 
i674 42 15—-4=7? 
Dee car 16 25 = 
oe Get li 6 32 
Sie Oe Fimo by Be al em 


S2. a. How many quart cans can be filled with fifteen pits 
of milk, and what will be left ? 

b. How many yard sticks can be cut from a fifteen-foot stick ? 

c. How many bushel baskets can be filled from fifteen pecks 
of apples? What will be left ? 


132 FIRST STEPS IN ARITHMETIC. 


d. How many gallon measures can be filled from fifteen quarts 
of milk? What will be left ? 


e. How many street-car rides can you take for fifteen cents ? 


f. Carrie has fifteen pinks; to how many girls can she give 
six pinks each, and how many pinks will she have left ? 


Cut a piece of paper or string fifteen inches long. Mark it in 
inches. 


g. If you cut it in inch pieces, how many pieces will you 
have? 


h. How many two-inch pieces will it cut into? 

7. How many three-inch pieces will it cut into ? 

7. How many four-inch pieces will it cut into ? 

k. How many five-inch pieces will it cut into ? 

/. How many six-inch pieces will it cut mto ? 

m. How many seven-inch pieces will it cut into ? 

n. If you cut off an eight-inch piece, what will be left ? 
. Fifteen divided by eight is how many ? 

. If you cut off a nine-inch piece, what will be left ? 
. Fifteen divided by nine is what ? 

. If you cut off a ten-inch piece, what will be left ? 
s. Fifteen divided by ten is how many ? 


Se Swe Sa 


Draw an oblong five inches long and three inches wide. 
Divide it into square inches. 


t. How many square inches in each row of the length? 
wu. How many such rows are there ? 


FIFTEEN. 183 


v. How many square inches in the oblong ? 
w. How many are three times five ? 

. What is one third of fifteen ? 

. How many are five times three ? 

What is one fifth of fifteen ? 


8 


xe 


WRITTEN EXERCISE. 


a. Fifteen quarts of milk will fill 
quarts. 


6. Fifteen pints of milk will fill 


gallon cans and leave 


quart cans, and leave 


bushel baskets and 


c. Fifteen pecks of potatoes will fill 
leave pecks, 


d. An oblong five inches long and three inches wide contains 
square inches. 


a hig a Ze OL oe et HED ca a fe 
Ot CY: ee My ee ne 
ema Limens <0? b+ 6=? Lee bie 
1+8=? 15+10=? Ui ot haat 
15+2=? 1+ 7=? 15+4=? 
Camere OL 15: —=i.0 4of15=°? e Of Lait 
erGle il, ==. eOl le a OL Lissie 


154 FIRST STEPS IN ARITHMETIC. 


SECTION XIV. 


SIXTEEN. 


S3. a. How many are ten and six? 

b. Eleven and how many are sixteen? 
c. Twelve and how many are sixteen ? 
d. Thirteen and how many are sixteen? 
e. Fourteen and how many are sixteen ? 


f. Fifteen and how many are sixteen ? 


g. Ten and how many are sixteen ? 

h. Nine and how many are sixteen ? 

i. Hight and how many are sixteen ? 

j. Seven and how many are sixteen ? 

k. Sixteen less seven are how many ? 

. Sixteen less nine are how many ? 

m. Sixteen less eight are how many ? 

n. What is one half of sixteen ? 

o. Make a number story about nine and seven. 


p. Make a number story about eight and eight. 


SIXTEEN. 135 


q. Make a number story about sixteen less seven. 
r. Make a number story about sixteen less nine. 
s. Make a number story about sixteen less eight. 
¢. Add at sight: 


Lt 9 13 8 10 14 15 12 
Ss 9 IE TAS I a SO ee ae 
wu. Subtract at sight: 

LO 16 16 16 16 16 16 16 
emt Fs ia Pe 
16 16 16 16 16 16 16 
e 10 Sy 14 5 12 as 


S4, a. Carrie picked nine roses and seven pinks; how many 
flowers did she pick ? 

6. John walked eight miles to see a friend and eight miles 
home again; how far did he walk ? | 

c. If Henry can ride eight miles an hour on his bicycle, how 
far can he ride in two hours ? 

d. If Laura had sixteen pinks and gave the teacher nine of 
them, how many had she left ? 

e. If George is nine years old, in how many years will he be 
sixteen ? } 


136 FIRST STEPS IN ARITHMETIC. 


jf. Henry is sixteen years old and Susie 1s seven years old; 
how much older is Henry than Susie ? 


g. A man has nine sheep and seven cows; how many animals 
has he ? 


h. How many are five and three and eight ? 
i. How many are four and five and seven ? 


j. George had four cents, his mother gave him four cents and 
he earned eight cents; how much money had he? 

k. Laura has five dolls, Mary has four dolls, and Carrie has 
seven dolls; how many dolls have they all? 


/. A man had sixteen horses and sold eight of them; how 
many had he left ? 


m. John earned sixteen cents and spent eight cents; how 
much had he left ? 


n. Jennie had sixteen cents; she spent five cents for a book 
and three cents for a pencil; how much had she left ? 


o. Henry had sixteen marbles; he gave away five of them and 
lost four; how many had he left ? 


p. George had sixteen books; he gave away three and sold 
four; how many had he left ? 


q. Think of two numbers that make sixteen. What are 
they ? 

r. Think of two numbers not alike that make sixteen. Take 
away the smaller. What is left? 


s. Think of two numbers not alike that make sixteen; take 
away the larger. What is left? 


187 


SIXTEEN. 


oD 


<9 | 


~| 


SI 


~| 


~| 


ay 


Sa 


1D 


co) 


Subtract : 
16 


16 . 16 16 16 16 16 


16 


an) 


Je} 


for) 


‘oom | 


a 


re 


16 


16 


16 


16 


16 


16 


16 


188 FIRST STEPS IN. ARITHMETIC. 
© ® 8 te] 
e e@ ) 8 
@® © oe © e® @ 
8 
8 @ 8 8 @ S 


S6. a. Add twos to sixteen. 
6. Sixteen is how many twos? 


c. How many are eight twos? five twos? three twos? six 
twos? four twos? two twos? seven twos? 


d. ‘Twelve is how many twos? Ten? Six? Eight? Four? 
Fourteen? Sixteen? 


e. At two cents each, what is the price of five apples? of six? 
of eight? of seven? of three? of four? of two? 


J. At two cents each, how many apples can be bought for eight 
cents? for twelve cents? for sixteen cents? for six cents? for 
fourteen cents? for four cents? for ten cents 2? 


g. Add threes to sixteen. 
h. Sixteen is how many threes ? 


7. How many are five threes? two threes? four threes? three 
threes ? 


J. Twelve is how many threes? Six? Nine? Fifteen? 


SIXTEEN. 139 


k. Seven is how many threes?, Four? Ten? Sixteen? 
Thirteen? Five? Eleven? Eight? Fourteen? 

/. At three cents each, what is the price of five oranges? of 
two ? of four? of three ? 

m. At three cents each, how many oranges can you buy for 
nine cents? for ten cents? for twelve cents? for fourteen cents ? 
for sixteen cents ? 

n. Add fours to sixteen. 

o. Sixteen is how many fours ? 

p. How many are four fours? two fours? three fours ? 

g. Twelve is how many fours?’ Hight? Sixteen ? 

7. How many feet have four dogs? two dogs? three dogs ? 

s. At four cents each, how many bananas can you buy for six- 
teen cents? for eight cents? for twelve cents? for seven cents? 
for ten cents? for fifteen cents ? 

¢. Sixteen is how many fives? 

u. Sixteen is how many sixes ? 

‘y. Sixteen is how many sevens ? 


w. Sixteen is how many eights ? 


ra OY BN, dis mo ase Goer DEN Bia? 
XA 7 Di ata f Hh dap 
i tent Toe, gaa e ey Cee a 
MX SS 2 GSD ies o 9x4—7 
o5en =? ie =? 95 a? 
y- 16+2=? 16+5=°? 16+6=? 
16 = 4= ¢; 16—-7=? 16—3= 7 


146—-8=? 


140 FIRST STEPS IN ARITHMETIC. 


& 14+—-2=—? 4+7=? 15+5=? 
12+3=? 9+38=? 12+2=? 
12+—+4=? 6+3=? 10 = 2 = 
12—-6=? 10+5=? ce Peerd raat fe 


Write these tables. 


S87. Cut a string sixteen inches long. Mark it off in inches. 
Fold it into halves. 


a. What is one half of sixteen inches ? 
b. Fold it again. Into how many parts is it folded now? 


What is the name of each part? What is 4 of 1? 
. What is one fourth of sixteen inches ? 


os? 


e. Fold it agam. Into how many parts is it folded now ? 

f. What is the name of each part? What is 4 of 1? 

g. What is one eighth of sixteen ? 

h. Straighten it out. Into how many two-inch pieces will it 
Clit teem Os Ace 

i. Into how many three-inch pieces will it cut? 16 +3 =? 

j. Into how many four-inch pieces will it cut? 16 +4 =? 

k, Into how many five-inch pieces will it cut? 16 +5 =? 

7. Into how many six-inch pieces will it cut? 16 + 6 =? 

m. Into how many seven-inch pieces will it cut? 16 +7 =? 

n. Into how many eight-inch pieces will it cut? 16 +8 =? 

0. Into how many nine-inch pieces will it cut? 16 +9 =? 


p. Into how many ten-inch pieces will it cut? 16 + 10 =? 


SIXTEEN. 141 


Cut a square of paper four inches on each side. Fold it into 
sixteen small squares. : 


q. How large is each small square ? 
Open it and fold it in halves. 


r. What is one half of sixteen square inches ? 

s. Fold it again. What is one fourth of sixteen square 
inches ? 

t. Fold it again. What is one eighth of sixteen square 
inches ? 

u. Fold it again. What part of the whole square do you see 
now ? 

v. What is 4 of 4? 

w. What is 2, of 16 square inches ? 

«. How many fourths equal one half? 

y. How many eighths equal one half? one fourth ? 


z. How many sixteenths equal one half? one fourth? one 
eighth ? 


ORAL AND WRITTEN EXERCISE. 


sof 16=? Wola li ae yz of 16 = ? 4x4=—? 
}of 16= ? ze OL h ty 7 of 16 = ? 8x2=? 
SOG =f fOfuhb =. 2 yg of 16=? Pip sR he 
16+2=? 16+5=? 16+ 8=? 
146+3=? 16+-6=? 146+ 9=? 


16+-4=>? 16+-7=°? 16+-10=? 


142 


FIRST STEPS IN ARITHMETIC. 


SECTION XV. 


SEVENTEEN, EIGHTEEN, AND NINETEEN. 


S8. a. What numbers do you already know that make 
seventeen ? 


6. What numbers do you already know that make eighteen ? 


ae 


so 


See SS 


7. 


nN. 


Nine and how many make seventeen ? 

Nine and how many make eighteen ? 

Take nine from seventeen; what is left ? 

Take nine from eighteen; what is left ? 

Take eight from seventeen ; what is left ? 
Make a number story about nine and eight. 
Make a number story about nine and nine. 
Make a number story about seventeen less nine, 
Make a number story about seventeen less eight. 
Make a number story about eighteen less nine. 
How many are two times nine ? 

What is one half of eighteen ? 


SEVENTEEN, EIGHTEEN, AND NINETEEN. 143 


o. Look at the nine and nine tablet. How many dots in each 
vertical row ? 

p. How many, vertical rows are there ? 

g. How many are three times six? 

r. What is one third of eighteen ? 

s. How many dots are in each horizontal row ? 

¢. How many horizontal rows are there ? 

u. How many are six times three ? 

v. What is one sixth of eighteen ? 


w, 918— 7? ea, 
ier pene. (peer 
liv— 9= 
t 6X8=? Lof 18 =? 
3x6=°? AOR mt 1 
2x9=? 1 of 18 =? 
9x2=? ; 


S9. a. Henry has nine books and George has eight books; 
how many books have they both ? 

6. Carrie has nine roses and nine pinks; how many flowers 
has she? 

c. A store-keeper has nine blue-eyed dolls and eight black-eyed 
dolls; how many dolls has he? 

d. One man has eighteen horses and another man has nine 
horses; how many more horses has the first man than the 
second ? 


144 FIRST STEPS (IN ARITHMETIC, 


e. In one field are seventeen sheep and in another field are 
eight sheep; how many more sheep are in the first field than in 
the second ? | 

jf. George had seventeen cents and spent nine cents; how 
many cents had he left ? 

g. John spent five cents for a top, four cents for a ball, and 
nine cents for a kite; how much money did he spend ? 

h. Jennie has three red pinks, five white ones, and nine pink 
ones; how many pinks has she ? 

i. Lucy had seventeen cents; she spent five cents for a book 
and four cents for a slate; how much money had she left ? 

jy. A lady had seventeen apples; she gave four apples to her 
little boy and four to her little girl; how many apples had she 
left ? 

k. A man had eighteen horses; he sold five of them to one 
man, and four of them to another man; how many horses had 
he left ? 

/. John has six marbles, Willie has three marbles, and Arthur 
has eight marbles; how many marbles have they all ? 

m. George is nine years old; in how many years will he be 
seventeen ? 

n. Mary is eight years old; in how many years will she be 
seventeen ? 

o. Jennie is nine years old; in how many years will she be 
eighteen ? 


p. Eighteen is how many more than nine? 


145 


SEVENTEEN, EIGHTEEN, AND NINETEEN, 


90. Add: 


co 


oD 


i) 


oO 


t 


N 


x 


1 | 


~ 


t~ 


N 


1a 


N 


re 


cO 


a4 


oD 


m= 


(oe) 


2 | 


Subtract: 


17 


17 


iY 


17 


1 


17 


17 


oD 


fo 6) 


a 


18 


18 


17 


17 


17 


17 


17 


17 


17 


ie.) 


Ven) 


ct 


oS 


N 


18 


18 


18 


18 


18 


18 


18 


18 


I 


Yon) 
rt 


H 


re 


18 


18 


18 


18 


18 


18 


oD 


t~ 


or 


146 FIRST STEPS IN ARITHMETIC. 


Pe a nea eee 
PAH cri 

RRR eRe: 
pace lee ee 


91. a. How many twos in seventeen ? 


b. At two cents each, how many apples could you buy for 
seventeen cents ? 


c. Seventeen is how many threes ? 
d. At three cents each, what is the price of five tops? 


e. How many tops at three cents each can you buy for seven- 
teen cents ? 


J. How many fours in seventeen ? 

g. How many pecks are there in four bushels ? 

h. Seventeen pecks are how many bushels ? 

z. How many fives are there in seventeen ? 

j. At five cents each, what is the cost of three balls? 


k. To how many persons could you give five cents each, if 


you had seventeen cents, and how many cents would you have 
left ? 


SEVENTEEN, EIGHTEEN, AND NINETEEN. 147 


7. How many sixes are in seventeen ? 

m. A lady gave six books to each of her two children; how 
many books did she give away ? 

n. If you had seventeen flowers, to how many people could 


you give six flowers each, and how many flowers would you have 
left ? 


o. How many sevens in seventeen ? 

p. How many days are there in two weeks ? 
q. Seventeen days are how many weeks ? 

r. How many eights in seventeen ? 

s. How many quarts are there in two pecks ? 
¢. Seventeen quarts are how many pecks? 

uw. How many nines in seventeen ? 


v. How many tens in seventeen ? 


wW. Bose ian? ea) oo 2xs8=? 
636-3)? 2x 6=? 
4x4? 2 ae 

een LO 2 —— 2 I Ee 16 = $=)! 
15—-3=? 12~—-6=/? 16 = =? 
144+—-4=? 14—7 = 16—10=? 

Yy AT+2=? 17 —5=—? 7-8 =? 
Liv = 5 —. ? Lie bie 17 = oeei:? 


7+—4=? Vist 2 1 jee AY 


148 FIRST STEPS IN ARITHMETIC. 


92, Find these out for yourselves : 


18+2=? 19 2 4 Ol: 1S sr 
18+3=°? 19+38=? tof 18=? 
18+4=? 19+4=? + Of 182.7 
18+5=? 19+5=? 40f 18=? 
18+6=? 19+6=? 
18+7=? 19 eae 
18+8=? 19+8=? 
183+9=>? 19+9=? 
18+10=>°? 19S eee 


93. a. At two cents each, how many tops can you buy for 
nineteen cents ? 


6. How many quarts are there in eighteen pints ? 

c. How many separate triangles can you lay with eighteen 
sticks ? 

d. At three cents each, how many pencils can you buy with 
nineteen cents ? 

e. How many gallons are eighteen quarts ? 

J. How many pecks are nineteen bushels ? 

g. If you have eighteen apples, to how many people can you 
give five apples each, and how many will you have left ? 

h. How many five-inch sticks can be cut from a nineteen- 
inch stick ? 

i. How many six-inch sticks can be cut from an eighteen-inch 
stick ? 


SEVENTEEN, EIGHTEEN, AND NINETEEN. 149 


j. At six cents each, how many flags can be bought for eigh- 
teen cents ? for nineteen cents ? 


k, Kighteen days are how many weeks ? 
1. Nineteen days are how many weeks ? 


m. At eight dollars each, how many chairs can be bought for 
eighteen dollars ? 

n. At eight cents each, how many kites can be bought for 
nineteen cents ? 

o. If a boy can ride nine miles an hour on a bicycle, how 
many hours will it take him to ride eighteen miles ? 

p. How many tables at nine dollars each can be bought for 
nineteen dollars ? 


g. If a man earns eighteen dollars in two weeks, how much 
does he earn in one week ? 

r. If a lady divided eighteen pencils equally among her three 
children, how many pencils did each one receive ? 

s. Henry had eighteen cents and spent one sixth of them; 
how much did he spend ? 


t. John had eighteen books and gave away one ninth of them; 
how many did he give away ? 


9A. REVIEW EXERCISES. 
Cie eye ees #5 nn a 
*] *9 #1 *3 *2 *5 * *2 *4 


ae *5 “I | AP *3 at gl] *2 *D 


150 


FIRST STEPS IN ARITHMETIC. 


*6 
*2 


a. Add at sight. 


b. Add, calling * in the upper number I. 


c. Add, calling * in the lower 


if) 


ate! 
* 4 


oy 
*4 


*9 
ie 


*3 


75 
wf 


hy 


#2 


a. Give remainders at sight. 


EG 


number l. 


3k 


*4 


ft 


b. Give remainders substituting 1 for * in upper number. 
ce. Give remainders substituting 1 for * in both numbers. 


TWENTY. 151 


SECTION XVI. 


TWENTY. 


95. a. What two numbers make ten ? 
b. What other two numbers make ten ? 
ce. What other two numbers make ten ? 
d. What other two numbers make ten ? 
e. What other two numbers make ten ? 


jf. Complete these additions, putting the numbers in place of * 
which will make the sums 10: 


| * om 
* 
Oo 


S| * wo 


g. How many are two tens ? 

h. If we made each of those upper numbers 10 larger, what 
would the answers be ? 

i. Complete these additions, putting the numbers in place of * 
which will make the sums 20: 


16 Le 19 18 15 14 4 13 12 
* * * * * * * * * 
20 20 20 20 20 20 20 20 20 

7. Subtract : 
10 10 10 10 10 10 1 10 10 
2 5 6 8 7 3 1 3 


152 FIRST STEPS@IN: ARITHMEDIC. 


k. Subtract: 
20 20 20 20 20 20 20 20 20 
2B 6 


i. Subtract, putting 1 in place of *: 


20 20 20 20 20 20 20 20 20 
#9 *5 ¥6 * *7 ¥4 *9 *] ¥3 


96. Draw an oblong five inches long and four inches wide. 
Divide it into square inches. 


Draw another oblong ten inches long and two inches wide. 
Divide it into square inches. 


a. How many square inches are in the first oblong ? 
b. How many square inches are in the second oblong ? 


Answer these questions, looking at the oblongs: 


c. How many are four times five ? 

d. How many are five times four ? 

e. How many are two times ten? 

jf. How many are ten times two? 

g. How many twos are there in twenty ? 
h. How many fours are there in twenty? 
1. How many fives are there in twenty ? 
j. How many tens are there in twenty ? 

k, What is one half of twenty ? 


MISCELLANEOUS REVIEW. 153 


7. What is one fourth of twenty ? 
m. What is one tenth of twenty ? 
n. What is one fifth of twenty ? 
Find these out for yourselves: 


20—+3=? 20—-7=? 20—-9=? 
20+6=? 20+-8=? 


SECTION XVII. 
MISCELLANEOUS REVIEW. 


97. Draw an inch square. Divide it into two equal parts. 


a, What is the name of each part ? 

b. How many halves are there in a square? in a circle? mm 
anything ? 

c. If half of anything is taken away, what is left ? 


Divide each half of the square into halves. 


d. Into how many parts is the square divided ? 

e. What is the name of each part ? 

jf. How many fourths in a square? in a circle? in anything? 

g. If one fourth of anything is taken away, what is left ? 

h. How many fourths are equal to one half ? 

i. If three fourths of anything are taken away, what is left ? 

Draw a square. Divide it into three equal parts by two 
vertical lines. | 


j- What is the name of each part ? 


154 FIRST STEPS IN ARITHMETIC. 


k. If one third of anything is taken away, what part of it is 
left ? 


i. If two thirds of anything are taken away, what part of it 1s 
left ? 


Draw a line five inches long. Divide it into five equal parts. 


m. What part of the line is one inch ? 
n. How many fifths are there in the whole of the line? 


o. Tf one fifth of anything is taken away, what part of it 1s 
left ? | 


p. Tf two fifths of anything are taken away, what part of it is 
left? four fifths? three fifths ? 


Draw a square. Divide it into three equal parts by two ver- 
tical lines, then draw the horizontal diameter. 


q. Into how many parts is the square divided ? 
yr. What is the name of each part? 


Draw a circle and divide it into sixths. 


s. How many sixths are there in the whole of anything? 
¢. How many sixths equal one half ? 
u. How many sixths equal one third ? 


v. If one sixth of anything is taken away, what part of it 1s 
left ? 


w. If five sixths of anything are taken away, what part of it 
is left ? : 
Draw a circle and divide it into eighths. 


Draw a square and divide it into eighths. 


MISCELLANEOUS REVIEW. 155 


xz. How many eighths are equal to one fourth ? 
y. How many eighths are equal to one half? 
z. How many eighths are in the whole of anything? 


ORAL AND WRITTEN EXERCISE. 


a. If anything is divided into two equal parts, each part is 
called one 
b. If anything is divided into three equal parts, each part is 
called one 
ec. If anything is divided into four equal parts, each part is 
called one 
d. If anything is divided into five equal parts, each part 1s 
called one 
e. If anything is divided into six equal parts, each part 1s 
called one 
f. Vf anything is divided into seven equal parts, each part 1s 
called one 
g. If anything is divided into eight equal parts, each part is 
called one 
h. If anything is divided into nine equal parts, each part 1s 
called one 
i. If anything is divided into ten equal parts, each part 1s 
called one 


b+}! 
1-4 


-- 


= 3 
=? $+ 
? 


- 

2 

= — ? 
emt 1 


Cott pla 
Ct BO 


oyipo | 
| 
2 


=: 
=e 
k. One fourth is what part of one half? 
I. One eighth is what part of one half? 


156 FIRST STEPS IN ARITHMETIC. 


m. One eighth is what part of one fourth ? 
n. One sixth is what part of one half? 

o. One sixth is what part of one third? 

p. One ninth is what part of one third ? 

g. One tenth is what part of one half ? 

ry. One tenth is what part of one fifth ? 


98. a. How many pints are there in a quart ? 

6. How many quarts are there in a gallon? 

c. How many quarts are there in a peck ? 

d. What sort of things do we measure in quarts? 

e. What sort of things do we measure in gallons ? 

f. What sort of things do we measure in pecks ? 

g. How many pecks are there in a bushel ? 

h, How many quarts are there in half a gallon ? 

i. How many pecks are there in half a bushel ? 

j. How many quarts are there in half a peck ? 

k. How many pecks are there in a fourth of a bushel ? 

7. How many quarts are there in a fourth of a peck? 

m. How many quarts are there in an eighth of a peck ? 

n. If sixteen apples are divided equally among eight boys, how 
many apples does each boy receive ? 

o. If fourteen pencils are divided equally among seven per- 
sons, how many pencils does each person receive ? 


p- If five chairs are worth fifteen dollars, what is each chair 
worth ? 


MISCELLANEOUS REVIEW. 157 


gq. If a man walked eighteen miles in six hours, how far did 
he walk each hour ? 


*. If eighteen bananas were divided equally among nine chil- 
dren, how many bananas did each child receive ? 


See or 4—=" s0f Sato For la=%% Pof1ls=7 
fee Olen Ole Ot FOL 18S 7 Pei LG 
eee ieee Ors? 2) ek OF 165 220 4 of 162 
Peerolelo eee Of 2 of lA ff ol 16 = 2 
Pee Olivia — tee OLS tk of Ia Te of 9 at 
Peres oi be etOhe oo FOF LO ate Of amare 
mer Olr a0 ated Ol oa se Of 20 = tv = oft bx? 
Gretta ete O20 8 eob” 6 tp of 20-7? 


QQ. ADDITION EXAMPLES. 


(Notr To Treacuers. — These examples added by giving results only, first of the 
two lower numbers, then of the whole, give a review of all of the primary combina- 
tions in number upon which higher additions depend.) 


a b c d e Ai g h D 
- 6 7 5 9 8 9 a 9 i) 

2 4 6 2 4 3 1 3 i) 

a 1 1 2 2 2 1 3 4S 
a b c d e Be g h i 
8 9 s 3 8 4 4 6 6 

3 4 2 1 4 2 8 3 
zh EES SUA SP a a 


158 FIRST STEPS IN ARITHMETIC. 


a b c d e si qe h D 
6 8 yi ) 3) 9 9 7 6 
6 5 9 4 1 4) 4 5 1 
3 5) 1 9) 8 Oo Rs 2 oy 
a b c d e ih g h i 
7 8 6 vi 4 8 pee ss 7 
2 2 1 1 1 5) 1 7 6 
4 3 5 3) 6 ae 2 1 4 
a b c d e ? g h 2 
) 3 5 9) fe 1 7 8 2 
7 2 6 7 5) 1 3 oO 8 
Me ee 


100. a. John is nine years old; in how many years will he 
be fifteen years old ? 

b. Carrie has eight books and Lucy has nine books; how 
many books have they both ? 

c. George rode eight miles in one hour and seven miles the 
next hour; how many miles did he ride in both hours * 

d. A man earned four dollars one day, three dollars the next 
day, and five dollars the next day. How much did he earn in 
the three days? | 

e. A farmer owns two horses, nine cows, and eight sheep ; 
how many animals has he ? 

jf. A man had fifteen cows and sold six of them; how many 


had he left ? 


MISCELLANEOUS REVIEW. 159 
g. George is eighteen years old and Henry is nine years old; 
how much older is George than Henry ? 
h. Walter rode seventeen miles in two hours; the first hour 
he rode eight miles; how far did he ride the second hour ? 


7. Lucy had seventeen roses; she gave six of them to her 
mother and six of them to her teacher; how many roses had she 
left ? 


j. A man had fifteen horses; he sold four of them to one 
man and five of them to another man; how many horses had he 


left ? 


k. John had sixteen cents; he spent seven cents for a top 
and six cents for a book; how much money had he left ? 


/. How far can a man walk in four hours if he walks three 
miles each hour ? F 


m. How many days are there in two weeks? 
n. How many quarts are there in two pecks ? 
0. How many feet long is a pole which is six yards long? 


p. If a man can walk three miles an hour, how many hours 
would it take him to walk eighteen miles ? 


g. At six cents each, how many kites can be bought for eigh- 
teen cents ? 


7. How many weeks are fourteen days ? 
s. How many bushels are sixteen pecks ? 


¢. Mary had fourteen pinks and gave one half of them to her 
sister ; how many pinks did she give her sister ? 


u. George had eighteen cents and spent one third of them for 
atop; what did the top cost ? 


160 FIRST STEPS IN ARITHMETIC. 


v. Henry paid sixteen cents for four books; what did each 
one cost ? 

w. Jennie had fifteen roses, and gave one fifth of them away ; 
how many did she give away? 

x. Lucy had twelve cents and spent half of them for candy ; 
how many cents had she left ? 

y. Walter had twelve cents; he spent one third of them for ink 

and the rest for paper; what did the paper cost? 

2. Willie had sixteen cents and spent one fourth of them; 
how many cents had he leit? 


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